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Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals

Download Big Ideas Math Answers Grade 5 Chapter 7 Divide Decimals PDF for free. Learn every topic of BIM Grade 5 Chapter 7 Divide Decimals Answers. Make use of our material and check out the step-by-step explanation to learn all the concepts easily. Enjoy the learning of maths with the help of our BIM Grade 5 Answer Key for Chapter 7 Divide Decimals. Our complete guide will help you to score the best marks in the exam and also in your preparation. Therefore, without any second thought prepare with Big Ideas Math Book 5th class Answer Key Chapter 7 Divide Decimals and get a good score in the exam.

Big Ideas Chapter 7 Divide Decimals 5th Grade Math Book Answer Key

Find the best tips that make your students love to practice maths and encourage them to use them for easy practicing. We have also provided different tricks to solve all the math problems. Big Ideas math 5th grade Chapter 7 Divide Decimals textbook Answer Key is the best source for the students. All the relevant links of Divide Decimals are given below. Check the links and begin your practice now.

Lesson: 1 Division Pattern with Decimals

Lesson 7.1 Division Pattern with Decimals

Division pattern with decimals homework & practice 7.1.

Lesson: 2 Estimate Decimals Quotients

Lesson 7.2 Estimate Decimals Quotients

Estimate decimals quotients homework & practice 7.2.

Lesson: 3 Use Models to Divide Decimals by Whole Numbers

Lesson 7.3 Use Models to Divide Decimals by Whole Numbers

Use models to divide decimals by whole numbers homework & practice 7.3.

Lesson: 4 Divide Decimals by One-Digit Numbers

Lesson 7.4 Divide Decimals by One-Digit Numbers

Divide decimals by one-digit numbers homework & practice 7.4.

Lesson: 5 Divide Decimals by Two-Digit Numbers

Lesson 7.5 Divide Decimals by Two-Digit Numbers

Divide decimals by two-digit numbers homework & practice 7.5.

Lesson: 6 Use Models to Divide Decimals

Lesson 7.6 Use Models to Divide Decimals

Use models to divide decimals homework & practice 7.6.

Lesson: 7 Divide Decimals

Lesson 7.7 Divide Decimals

Divide decimals homework & practice 7.7.

Lesson: 8 Insert Zeros in the Dividend

Lesson 7.8 Insert Zeros in the Dividend

Insert zeros in the dividend homework & practice 7.8.

Lesson: 9 Problem Solving: Decimal Operations

Lesson 7.9 Problem Solving: Decimal Operations

Problem solving: decimal operations homework & practice 7.9.

Chapter: 7 – Divide Decimals

Divide Decimals Performance Task

Divide decimals activity, divide decimals chapter practice.

Explore and Grow

Describe the placement of the decimal point when dividing a decimal by 10, 100, 0.1, and 0.01. Answer:

Think and Grow: Division Pattern with Decimals

Show and Grow

Find the quotient. Question 1. 62.5 ÷ 10 2 = ______ Answer: 0.625 Explanation:  First Simplify the 10 2 which means  10X10 =100 then we need to calculate the fraction to a decimal just divide the numerator(62.5) by the denominator (100): 62.5 ÷ 100 =0.625 so,  62.5/100 =0.625 Question 2. 1.84 ÷ 0.1 = ______ Answer: 18.4 Explanation: To convert this simple fraction to a decimal just divide the numerator (1.84) by the denominator (0.1): 1.84 ÷ 0.1 = 18.4 so, 1.84/0.1 = 18.4

Apply and Grow: Practice

Find the quotient. Question 3. 76 ÷ 10 = ______ Answer:  7.6 Explanation: To convert this simple fraction to a decimal just divide the numerator (76) by the denominator (10): 76 ÷ 10 = 7.6 so, 76/10 = 7.6 Question 4. 3.65 ÷ 0.1 = _______ Answer: 36.5 Explanation: To convert this simple fraction to a decimal just divide the numerator (3.65) by the denominator (0.1): 3.65 ÷ 0.1 = 36.5. so, 3.65/0.1 = 36.5 Question 5. 2.9 ÷ 0.01 = ______ Answer: 290 Explanation: To convert this simple fraction to a decimal just divide the numerator (2.9) by the denominator (0.01): 2.9 ÷ 0.01 = 290. so, 2.9/0.01 = 290 Question 6. 18.7 ÷ 10 2 = ______ Answer: 0.187 Explanation: First Simplify the 10 2 which means  10X10 =100 then we need to calculate the fraction to a decimal just divide the numerator(18.7) by the denominator (100): 18.7 ÷ 100 =0.187 so,  18.7/100 =0.187

49 ÷ b = 0.49

1.3 ÷ b = 0.013

For these two equations b value should be 100.

Question 12. YOU BE THE TEACHER Your friend says 8,705 ÷ 10 3 is equivalent 8,705 × 0.001. Is your friend correct? Explain. Answer:

8,705 ÷ 10 3

Think and Grow: Modeling Real Life

Question 13. An art teacher has 68.5 pounds of clay and orders 56.5 more pounds. The teacher equally divides the clay among 100 students. How much clay does each student get? Answer: To find how much clay each student get, divide the sum of the clay by 100. Add the quantities of the clay. 68.5 + 56.5 = 125 Divide the total clay by 100. Dividing 125 by 100, or 10 2 125 ÷ 100 = 125 ÷ 10 2 = 1.25 Each student gets 1.25 pounds clay.

Find the quotient. Question 1. 810 ÷ 10 = ______ Answer: 81

Explanation: To convert this simple fraction to a decimal just divide the numerator (810) by the denominator (10): When we divide by 10, the decimal point moves one place to the left. 810 ÷ 10 = 81.

Question 2. 7.4 ÷ 0.01 = ______ Answer: 740

Explanation: To convert this simple fraction to a decimal just divide the numerator (7.4) by the denominator (0.01). When we divide by 0.01, the decimal point moves two places to the right. : 7.4 ÷ 0.01 = 740.

Question 3. 903 ÷ 10 3 = ______ Answer: 0.903

First Simplify the 10 3 which means  10 x 10 x 10 =1000, then we need to calculate the fraction to a decimal just divide the numerator (903) by the denominator (1000). When we divide by 1000, the decimal point moves three places to the left.

Question 4. 267.1 ÷ 0.01 = ______ Answer: 26710

Explanation: To convert this simple fraction to a decimal just divide the numerator (267.1) by the denominator (0.01). When we divide by 0.01, the decimal point moves two places to the right : 267.1 ÷ 0.01 = 26710

Question 5. 5.6 ÷ 0.1 = ______ Answer: 56

Explanation: To convert this simple fraction to a decimal just divide the numerator (5.6) by the denominator (0.1). When we divide by 0.1, the decimal point moves one place to the right : 5.6 ÷ 0.1 = 56

Question 6. 0.4 ÷ 10 2 = ______ Answer: 0.004

First Simplify the 10 2 which means  10 x 10 = 100, then we need to calculate the fraction to a decimal just divide the numerator (0.4) by the denominator (100). When we divide by 100, the decimal point moves two places to the left : 0.4 ÷ 100 = 0.004

Find the value of k. Question 7. 89 ÷ k = 8.9 Answer: k = 10

Explanation: Lets solve your equation step by step 89 ÷ k = 8.9 Multiply both sides by K. 89 = 8.9 K 8.9 K = 89 (Flip the equation)

Question 8. k ÷ 0.01 = 36 Answer: k = 0.36

Question 9. 72.4 ÷ 0.724 Answer: 100

To convert this simple fraction to a decimal just divide the numerator (72.4) by the denominator (0.724).

Question 11. Patterns How does the value of a number change when you divide by 10? 100? 1,000? Answer: When we divide by 10, the decimal point moves one place to the left. When we divide by 100, the decimal point moves two places to the left. When we divide by 1000, the decimal point moves three places to the left.

Question 12. Writing How can you determine where to place the decimal point when dividing 61 by 1,000? Answer:

Question 14. Modeling Real Life A family buys 2 personal watercrafts for $3,495 each. The family makes 10 equal payments for the watercrafts. What is the amount of each payment? Answer: To find amount of each payment, divide the sum of the personal watercrafts by 10. Add 2 personal watercrafts. 3,495 + 3,495 = 6990 Divide the total sum by 10. Dividing 6990 by 10, or 10 1 6990 ÷ 10 = 6990 ÷ 10 1 = 699 So, the amount of each payment = $699.

Question 15. Modeling Real Life A group of people attempts to bake the largest vegan cake. They use 17 kilograms of cocoa powder, which is one-tenth the amount of kilograms of dates they use. How many kilograms of cocoa power and dates do they use altogether? Answer: Cocoa powder = 17 kilograms Let dates amount = d (1/10)d = 17 dates(d) = 17 x 10 = 170 kilograms Sum of cocoa power and dates = 17 + 170 = 187 kilograms

Review & Refresh

Find the sum or difference. Question 16. 0.75 – 0.23 = ______ Answer: 0.52

Question 17. 1.46 + 1.97 = ______ Answer: 3.43

Think and Grow: Estimate Decimals Quotients

Example Estimate 4.2 ÷ 8. Rename 4.2 as tenths. 4.2 is 42 tenths. 42 tenths is close to40 tenths. 40 and 8 are compatible numbers. 40 tenths ÷ 8 = _______ tenths, or ______ So, 4.2 ÷ 8 is about ______.

Estimate the quotient. Question 1. 17.4 ÷ 3.1 Answer: Round the divisor 3.1 to 3. Think: What numbers close to 17.4 are easily divided by 3? Use 18. 18 ÷ 3 = 6 So, 17.4 ÷ 3.1 is about 6.

Question 2. 57.5 ÷ 6.89 Answer: Round the divisor 6.89 to 7. Think: What numbers close to 57.5 are easily divided by 7? Use 56. 56 ÷ 7 = 8 So, 57.5 ÷ 6.89 is about 8.

Question 3. 3.7 ÷ 5 Answer: Rename 3.7 as tenths 3.7 is 37 tenths. 37 is close to 35. 35 tenths ÷ 5 = 7 tenths or 0.7 So, 3.7 ÷ 5 is about 0.7

Question 4. 25.8 ÷ 30 Answer: Rename 25.8 as tenths 25.8 is 258 tenths. 258 is close to 270. 270 tenths ÷ 30 = 9 tenths or 0.9 So, 25.8 ÷ 30 is about 0.9

Estimate the quotient. Question 5. 3.5 ÷ 6 Answer: Rename 3.5 as tenths 3.5 is 35 tenths. 35 is close to 36. 36 tenths ÷ 6 = 6 tenths or 0.6 So, 3.5 ÷ 6 is about 0.6

Question 6. 1.87 ÷ 9 Answer: Rename 1.87 as tenths 1.87 is 18.7 tenths. 18.7 is close to 18. 18 tenths ÷ 9 = 2 tenths or 0.2 So, 1.87 ÷ 9 is about 0.2

Question 7. 46 ÷ 2.3 Answer: Round the divisor 2.3 to 2. 46 ÷ 2 = 23

Question 8. 31.1 ÷ 6.5 Answer: Round the divisor 6.5 to 6. 31.1 is closer to 30. 30 ÷ 6 = 5 So, 31.1 ÷ 6.5 is about 5.

Question 9. 91.08 ÷ 5.2 Answer: Round the divisor 5.2 to 5. 91.08 is closer to 90. 90 ÷ 5 = 18 So, 91.08 ÷ 5.2 is about 18.

Question 10. 137.14 ÷ 12.2 Answer: Round the divisor 12.2 to 12. 137.14 is closer to 144. 12 and 144 are compatible numbers. 144 ÷ 12 = 12 So, 137.14 ÷ 12.2 is about 12.

Question 12. Reasoning Descartes estimates 43.2 ÷ 7.3 using mental math. Do you think he uses 43 ÷ 7 or 42 ÷ 7? Explain. Answer: Round the divisor 7.3 to 7 Think: What numbers close to 43.2 are easily divided by 7? Use 42. 42 and 7 are compatible numbers. 42 ÷ 7 = 6 So, 42 ÷ 7 is correct.

Question 13. DIG DEEPER! Describe a division situation in which an estimate of two decimals is appropriate. Answer:

Question 15. A fish tank pump filters 158.5 gallons of water each hour. About how many gallons of water does the pump filter each minute? Answer: Fish tank pump filters 158.5 gallons of water 1 hour = 60 minutes Think: What numbers close to 158.5 are easily divided by 60? Use 180 180 ÷ 60 = 3 Pump filters about 3 gallons of water each minute.

Question 16. DIG DEEPER! A group of 32 students goes to a museum and a play. The total cost for the museum is $358.98 and the total cost for the play is $256.48. About how much does it cost for each student to go to the museum and the play? Answer: Cost for museum = $358.98 Cost for the play = $256.48 358.98 + 256.48 = $615.46 Think: What numbers close to 615.46 are easily divided by 32? Use 608. It is closer to 615.46 608 ÷ 32 = $19 Each student go to the museum and the play costs about $19.

Estimate the quotient. Question 1. 2.3 ÷ 6 Answer: Rename 2.3 as tenths 2.3 is 23 tenths. 23 is close to 24. 24 tenths ÷ 6 = 4 tenths or 0.4 So, 2.3 ÷ 6 is about 0.4

Question 2. 1.67 ÷ 8 Answer: Rename 1.67 as hundredths 1.67 is 167 hundredths. 167 is close to 168. 168 hundredths ÷ 8 = 21 hundredths or 0.21 So, 1.67 ÷ 8 is about 0.21

Question 3. 28 ÷ 4.7 Answer: Round the divisor 4.7 to 5 28 is closer to 30 30 ÷ 5 = 6 So, 28 ÷ 4.7 is about 6.

Question 4. 13.8 ÷ 4.9 Answer: Round the divisor 4.9 to 5 Think: What numbers close to 13.8 are easily divided by 5? Use 15. 15 ÷ 5 = 3 So, 13.8 ÷ 4.9 is about 3.

Question 5. 42.1 ÷ 7.3 Answer: Round the divisor 7.3 to 7 Think: What numbers close to 42.1 are easily divided by 7? Use 42. 42 ÷ 7 = 6 So, 42.1 ÷ 7.3 is about 6.

Question 6. 201.94 ÷ 18.1 Answer: Round the divisor 18.1 to 18 Think: What numbers close to 201.94 are easily divided by 18? Use 198. 198 ÷ 18 = 11 So, 201.94 ÷ 18.1 is about 11.

Question 8. Reasoning A family used 9.8 gallons of gasoline to drive 275.5 miles. To determine how far they drove using one gallon of gasoline, can they use an estimate, or is an exact answer required? Explain. Answer: Given that, 9.8 gallons of gasoline drives = 275.5 miles 1 gallon = 275.5 ÷ 9.8 Divisor 9.8 is rounded to 10. 275.5 is closer to 276. 276 ÷ 10 is about 27.6

Question 9. YOU BE THE TEACHER Your friend says 9 ÷ 2.5 is about 3. Is your friend’s estimate reasonable? Explain. Answer: Round the divisor 2.5 to 3. 9 ÷ 3 =3 So, my friend’s estimate is reasonable.

Number Sense Without calculating, tell whether the quotient is greater than or less than 1. Explain. Question 10. 4.58 ÷ 0.3 Answer: When the dividend is greater than the divisor, the quotient is greater than 1.

Question 11. 0.6 ÷ 12 Answer: When the divisor is greater than the dividend, the quotient is less than 1.

Find the product. Check whether your answer is reasonable. Question 14. 56 × 78 = _____ Answer: 4368

Question 15. 902 × 27 = ______ Answer: 24,354

Question 16. 4,602 × 35 = _______ Answer: 1,61,070

Reasoning When you divide a decimal by a whole number, what does the quotient represent? Answer:

Think and Grow: Use Models to Divide Decimals

Use a model to find the quotient. Question 4. 1.5 ÷ 3 Answer: Think: 1.5 is 1 ones and 5 tenths 15 tenths can be divided equally as 3 groups of 5 tenths. So, 1.5 ÷ 3 = 5 tenths = 0.5

Question 5. 2.7 ÷ 9 Answer: Think: 2.7 is 2 ones and 7 tenths 27 tenths can be divided equally as 9 groups of 3 tenths. So, 2.7 ÷ 9 = 3 tenths = 0.3

Question 6. 1.44 ÷ 8 Answer: Think: 1.44 is 1 ones, 4 tenth and 4 hundredths. 14 tenths can be divided equally as 8 groups So, 144 hundredths can be divided equally as 8 groups So, 1.44 ÷ 8 = 0.18

Question 7. 3.12 ÷ 6 Answer: Think: 3.12 is 3 ones, 1 tenth and 2 hundredths. 31 tenths can be divided equally as 6 groups So, 312 hundredths can be divided equally as 6 groups So, 3.12 ÷ 6 = 0.52

Question 8. Reasoning Do you start dividing the ones first when finding 5.95 ÷ 7? Explain. Answer: Think: 5.95 is 5 ones, 9 tenth and 5 hundredths. We have to start dividing the tenths first because 5 ones is less than 7. 59 tenths can be divided equally as 7 groups So, 595 hundredths can be divided equally as 7 groups So, 5.95 ÷ 7 = 0.85

Question 9. Number Sense Without dividing, determine whether the quotient of 9.85 and 5 is greater than or less than 2. Explain. Answer: Quotient of 9.85 and 5 is less than 2, because 5 x 2 =10 and 9.85 is less than 10.

Question 11. DIG DEEPER! You pay $5.49 for 3 pounds of plums and $6.36 for 4 pounds of peaches. Which fruit costs more per pound? How much more? Answer: Think: 5.49 is 5 ones, 4 tenths and 9 hundredths. 5 ones can be divided equally as 3 groups of 1 ones with remainder 2. Remainder has to place before 4 tenths. 24 tenths can be divided equally as 3 groups of 8 tenths 9 hundredths can be divided equally as 3 groups of 3 hundredths So, 549 hundredths can be divided equally as 3 groups of 183 hundredths. Plums = 5.49 ÷ 3 = 1.83 Think: 6.36 is 6 ones, 3 tenths and 6 hundredths. 6 ones can be divided equally as 4 groups of 1 ones with remainder 2. Remainder has to place before 3 tenths. 23 tenths can be divided equally as 4 groups of 5 tenths with remainder 3. Remainder has to place before 6 hundredths. 36 hundredths can be divided equally as 4 groups of 9 hundredths So, 636 hundredths can be divided equally as 4 groups of 159 hundredths. Peaches = 6.36 ÷ 4 = 1.59 1.83 – 1.59 = 0.24 So, plums costs 0.24 more per pound than peaches.

Use a model to find the quotient. Question 3. 1.6 ÷ 8 Answer: Think: 1.6 is 1 ones and 6 tenths 16 tenths can be divided equally as 8 groups of 2 tenths . So, 1.6 ÷ 8 = 2 tenths = 0.2

Question 4. 2.1 ÷ 7 Answer: Think: 2.1 is 2 ones and 1 tenths 21 tenths can be divided equally as 7 groups of 3 tenths . So, 2.1 ÷ 7 = 3tenths = 0.3

Question 5. 1.56 ÷ 2 Answer: Think: 1.56 is 1 ones, 5 tenths and 6 hundredths. 15 tenths can be divided equally as 2 groups of 7 tenths with remainder 1. Remainder has to place before 6 hundredths. 16 hundredths can be divided equally as 2 groups of 8 hundredths . So, 156 hundredths can be divided equally as 2 groups of 78 hundredths. 1.56 ÷ 2 = 0.78

Question 6. 2.84 ÷ 4 Answer: Think: 2.84 is 2 ones, 8 tenths and 4 hundredths. 28 tenths can be divided equally as 4 groups of 7 tenths. 4 hundredths can be divided equally as 4 groups of 1 hundredths. So, 284 hundredths can be divided equally as 4 groups of 71 hundredths. 2.84 ÷ 4 = 0.71

Question 8. Writing Explain how dividing a decimal by a whole number is similar to dividing a whole number by a whole number. Answer: When dividing a decimal by a whole number, f irst we will  divide  the  decimal  by the  whole number  ignoring  decimal  point. Now put the  decimal point in the quotient same as the   decimal places in the dividend. So , dividing a decimal by a whole number is similar to dividing a whole number by a whole number.

Question 9. Modeling Real Life A designer learns there are 5.08 centimeters in 2 inches. How many centimeters are in 1 inch? Answer: 5.08 ÷ 2 Think: 5.08 is 5 ones, 0 tenths and 8 hundredths. 50 tenths can be divided equally as 2 groups of 25 tenths. 8 hundredths can be divided equally as 2 groups of 4 hundredths. So, 508 hundredths can be divided equally as 2 groups of 254 hundredths. So, 2.54 cm are in 1 inch.

Question 10. Modeling Real Life Newton buys 4 gallons of gasoline. He pays $8.64. How much does 1 gallon of gasoline cost? Answer: 8.64 ÷ 4 Think: 8.64 is 8 ones, 6 tenths and 4 hundredths. 8 ones can be divided equally as 4 groups of 2 ones. 6 tenths can be divided equally as 4 groups of 1 tenths with remainder 2. Remainder has to place before 4 hundredths. 24 hundredths can be divided equally as 4 groups of 6 hundredths. So, 864 hundredths can be divided equally as 4 groups of 216 hundredths. 1 gallon of gasoline cost is 216 hundredths = $2.16

Find the product. Explain the strategy you used. Question 11. 0.9 × 1.1 = ______ Answer: First multiply 9 x 11 = 99, then put the  decimal point in the answer as sum of the decimal places in the both numbers. decimal places = 1 + 1 = 2 99 after putting decimal places = 0.99

Question 12. 1.2 × 2.7 = ______ Answer: First multiply 12 x 27 = 324 then put the  decimal point in the answer as sum of the decimal places in the both numbers. decimal places = 1 + 1 = 2 324 after putting decimal places = 3.24

Question 13. 1.4 × 0.8 = ______ Answer: 1.12

Reasoning How is dividing decimals by one-digit whole numbers similar to dividing whole numbers? Answer:

Think and Grow: Divide Decimals by One-Digit Numbers

Find the quotient. Then check your answer. Question 1. \(\sqrt [ 2 ]{ 9.16 } \) Answer: Divide the ones 9 ÷ 2 4 ones x 2 = 8 9 ones – 8 ones There are 1 ones left over. Divide the tenths 116 ÷ 2 58 tenths x 2 116 – 116 = 0 There are 0 tenths left over. So, 9.16 ÷ 2 = 4.58

Question 2. \(\sqrt [ 5 ]{ 23.5 } \) Answer: Divide the ones 23 ÷ 5 4 ones x 5 = 20 23 ones – 20 ones There are 3 ones left over. Divide the tenths 35 ÷ 5 7 tenths x 5 35 – 35 = 0 There are 0 tenths left over. So, 23.5 ÷ 5 = 4.7

Question 3. \(\sqrt [ 3 ]{ 6.27 } \) Answer: Divide the ones 6 ÷ 3 2 ones x 3 = 6 6 ones – 6 ones There are 0 ones left over. Divide the tenths 27 ÷ 3 9 tenths x 3 27 – 27 = 0 There are 0 tenths left over. So, 6.27 ÷ 3 = 2.09

Find the quotient. Then check your answer. Question 4. \(\sqrt [ 4 ]{ 16.8 } \) Answer: Divide the ones 16 ÷ 4 4 ones x 4 = 16 16 ones – 16 ones There are 0 ones left over. Divide the tenths 8 ÷ 4 2 tenths x 4 8 – 8 = 0 There are 0 tenths left over. So, 16.8 ÷ 4 = 4.2

Question 5. \(\sqrt [ 9 ]{ 1.53 } \) Answer: Divide the tenths 15 ÷ 9 1 tenths x 9 15 – 9 = 6 There are 6 tenths left over. Divide the hundredths 63 ÷ 9 = 7 hundredths So, 1.53 ÷ 9 = 0.17

Question 6. \(\sqrt [ 5 ]{ 82.5 } \) Answer: Divide the ones 82 ÷ 5 16 ones x 5 = 80 82 ones – 80 ones There are 2 ones left over. Divide the tenths 25 ÷ 5 5 tenths x 5 25 – 25 = 0 There are 0 tenths left over. So, 82.5 ÷ 5 = 16.5

Question 7. 77.4 ÷ 3 = ______ Answer: Divide the ones 77 ÷ 3 25 ones x 3 = 75 77 ones – 75 ones There are 2 ones left over. Divide the tenths 24 ÷ 3 8 tenths x 3 24 – 24 = 0 There are 0 tenths left over. So, 77.4 ÷ 3 = 25.8

Question 8. 113.6 ÷ 8 = ______ Answer: Divide the ones 113 ÷ 8 14 ones x 8 = 112 113 ones – 112 ones There are 1 ones left over. Divide the tenths 16 ÷ 8 2 tenths x 8 16 – 16 = 0 There are 0 tenths left over. So, 113.6 ÷ 8 = 14.2

Question 9. 129.43 ÷ 7 = ______ Answer: Divide the ones 129 ÷ 7 18 ones x 7 = 126 129 ones – 126 ones There are 3 ones left over. Divide the tenths 34 ÷ 7 4 tenths x 7 34 – 28 = 6 There are 6 tenths left over. Divide the hundredths 63 ÷ 7 = 9 hundredths So, 129.43 ÷ 7 = 18.49

Find the value of y. Question 10. y ÷ 2 = 4.8 Answer: y = 4.8 x 2 y = 9.6

Question 11. 6.05 ÷ 5 = y Answer: 6.05 ÷ 5 Divide the ones 1 ones x 5 = 5 6 ones – 5 ones There are 1 ones left over. Divide the tenths 105 ÷ 5 21 tenths x 5 105 – 105 = 0 There are 0 tenths left over. So, 6.05 ÷ 5 = 1.21 y = 1.21

Question 12. y ÷ 8 = 4.29 Answer: y = 4.29 x 8 y = 34.32

Question 13. Reasoning Newton finds 75.15 ÷ 9. In what place is the first digit of the quotient? Explain. Answer: 75.15 ÷ 9 Divide the ones 75 ÷ 9 8 ones x 9 = 72 75 ones – 72 ones There are 3 ones left over. Divide the tenths 31 ÷ 9 3 tenths x 9 31 – 27= 4 There are 4 tenths left over. Divide the hundredths 45 ÷ 9 = 5 hundredths 75.15 ÷ 9 = 8.35, here quotient is in ones place .

Question 17. DIG DEEPER! A customer saves $9.24 by buying the set rather than buying them individually. What is one flying disc priced individually? Answer:

Find the quotient. Then check your answer. Question 1. \(\sqrt [ 3 ]{ 9.6 } \) Answer: Divide the ones 9 ÷ 3 3 ones x 3 = 9 9 ones – 9 ones There are 0 ones left over. Divide the tenths 6 ÷ 3 2 tenths x 3 6 – 6 = 0 There are 0 tenths left over. So, 9.6 ÷ 3 = 3.2.

Question 2. \(\sqrt [ 6 ]{ 7.56 } \) Answer: Divide the ones 7 ÷ 6 1 ones x 6 = 6 7 ones – 6 ones There are 1 ones left over. Divide the tenths 15 ÷ 6 2 tenths x 6 15 – 12 = 3 There are 3 tenths left over. Divide the hundredths 36 ÷ 6 = 6 hundredths. So, 7.56 ÷ 6 = 1.26.

Question 3. \(\sqrt [ 8 ]{ 42.4 } \) Answer: Divide the ones 42 ÷ 8 5 ones x 8 = 40 42 ones – 40 ones There are 2 ones left over. Divide the tenths 24 ÷ 8 3 tenths x 8 24 – 24 = 0 There are 0 tenths left over. So, 42.4 ÷ 8 = 5.3.

Question 4. 63.6 ÷ 4 = ______ Answer: Divide the ones 63 ÷ 4 15 ones x 4 = 60 63 ones – 60 ones There are 3 ones left over. Divide the tenths 36 ÷ 4 9 tenths x 4 36 – 36 = 0 There are 0 tenths left over. 63.6 ÷ 4 = 15.9

Question 5. 15.68 ÷ 7 = ______ Answer: Divide the ones 15 ÷ 7 2 ones x 7 = 14 15 ones – 14 ones There are 1 ones left over. Divide the tenths 16 ÷ 7 2 tenths x 7 16 – 14 = 2 There are 2 tenths left over. Divide the hundredths 28 ÷ 7 = 4 hundredths 15.68 ÷ 7 = 2.24

Question 6. 143.82 ÷ 9 = _______ Answer: Divide the ones 143 ÷ 9 15 ones x 9 = 135 143 ones – 135 ones There are 8 ones left over. Divide the tenths 88 ÷ 9 9 tenths x 9 88 – 81 = 7 There are 7 tenths left over. Divide the hundredths 72 ÷ 9 = 8 hundredths 143.82 ÷ 9 = 15.98

Find the value of y. Question 7. y ÷ 6 = 7.8 Answer: y = 7.8 x 6 y= 46.8

Question 8. 14.9 ÷ 5 = y Answer: Divide the ones 14 ÷ 5 2 ones x 5 = 10 14 ones – 10 ones There are 4 ones left over. Divide the tenths 49 ÷ 5 9 tenths x 5 49 – 45 = 4 There are 4 tenths left over. Divide the hundredths 40 ÷ 5 = 8 hundredths 14.9 ÷ 5 = 2.98 y = 2.98

Question 9. y ÷ 2 = 4.7 Answer: y = 4.7 x 2 y = 9.4

Question 10. Number Sense Evaluate the expression. (213.3 – 95.7) ÷ 8 Answer: (213.3 – 95.7) ÷ 8 = 117.6 ÷ 8 Divide the ones 117 ÷ 8 14 ones x 8 = 112 117 ones – 112 ones There are 5 ones left over. Divide the tenths 56 ÷ 8 7 tenths x 8 56 – 56 = 0 There are 0 tenths left over. (213.3 – 95.7) ÷ 8 = 117.6 ÷ 8 = 14.7

Question 11. Writing Write and solve a real-life problem that involves dividing a decimal by a whole number. Answer: In 5 minutes John eats 7.5 chocolates.  how many chocolates can he eat in one minute? 7.5 ÷ 5 Divide the ones 7 ÷ 5 1 ones x 5 = 5 7 ones – 5 ones There are 2 ones left over. Divide the tenths 25 ÷ 5 = 5 tenths 7.5 ÷ 5 = 1.5 In 1 minute, he can eat 1.5 chocolates.

Question 13. Modeling Real Life You buy 2 packages of ground beef. One package contains 4.5 pounds and the other contains 2.25 pounds. You put equal amounts of meat into 9 freezer bags. How many pounds of meat are in each bag? Answer: To find many pounds of meat are in each bag, divide the total meat by 9. Add the two packages of meat. 4.5 + 2.25 = 6.75 6.75 ÷ 9 Divide the tenths 67 ÷ 9 7 tenths x 9 = 63 67 tenths – 63 tenths There are 4 tenths left over. Divide the hundredths 45 ÷ 9 = 5 hundredths 6.75 ÷ 9 = 0.75

Use partial quotients to divide. Question 15. 607 ÷ 15 = ______ Answer: 15 x 40 = 600 with remainder 7.

Question 16. 4,591 ÷ 33 = ______ Answer:

Question 17. 6,699 ÷ 87 = ______ Answer: 87 x 50 = 4350 6,699 – 4350 = 2349 87 x 20 = 1740 2349 – 1740 = 609 87 x 5 = 435 609 – 435 = 174 87 x 2 = 174 6,699 ÷ 87 = 50 + 20 + 5 + 2 = 77.

Precision Explain how you can use estimation to check your answers. Answer:

Think and Grow: Divide Decimals by Two-Digit Numbers

Find the quotient. Then check your answer. Question 1. \(\sqrt [ 12 ]{ 51.6 } \) Answer: Divide the ones 51 ÷ 12 4 ones x 12 = 48 51 ones – 48 ones There are 3 ones left over. Divide the tenths 36 ÷ 12 3 tenths x 12 = 36 36 – 36 = 0 There are 0 tenths left over. So, 51.6 ÷ 12 = 4.3

Question 2. \(\sqrt [ 17 ]{ 140.25 } \) Answer: Divide the ones 140 ÷ 17 8 ones x 17 = 136 140 ones – 136 ones There are 4 ones left over. Divide the tenths 42 ÷ 17 2 tenths x 17 = 34 42 – 34 = 8 There are 8 tenths left over. Divide the hundredths 85 ÷ 17 = 5 hundredths. So, 140.25 ÷ 17 = 8.25

Question 3. \(\sqrt [ 61 ]{ 32.33 } \) Answer: Divide the tenths 323 ÷ 61 5 ones x 61 = 305 323 tenths – 305 tenths There are 18 tenths left over. Divide the hundredths 183 ÷ 61 = 3 hundredths So, 32.33 ÷ 61 = 0.53

Place a decimal point where it belongs in the quotient. Question 4. 251.75 ÷ 19 = 1 3 . 2 5 Answer: When dividing a decimal by a whole number, f irst we will  divide  the  decimal  by the  whole number  ignoring  decimal  point. Now put the  decimal point in the quotient same as the   decimal places in the dividend.

Question 5. 88.04 ÷ 62 = 1 . 4 2 Answer:

Question 6. 3.22 ÷ 23 = 0 .1 4 Answer:

Find the quotient. Then check your answer. Question 7. \(\sqrt [ 54 ]{ 97.2 } \) Answer: Divide the ones 97 ÷ 54 1 ones x 54 = 54 97 ones – 54 ones There are 43 ones left over. Divide the tenths 432 ÷ 54 = 8 tenths So, 97.2 ÷ 54 = 1.8

Question 8. \(\sqrt [ 91 ]{ 200.2 } \) Answer: Divide the ones 200 ÷ 91 2 ones x 91 = 182 200 ones – 182 ones There are 18 ones left over. Divide the tenths 182 ÷ 91 = 2 tenths So, 200.2 ÷ 91 = 2.2

Question 9. \(\sqrt [ 2 ]{ 56.2 } \) Answer: Divide the ones 56 ÷ 2 28 ones x 2 = 56 56 ones – 56 ones There are 0 ones left over. Divide the tenths 2 ÷ 2 = 1 tenths So, 56.2 ÷ 2 = 28.1

Question 10. 6.08 ÷ 16 = _____ Answer: Divide the tenths 60 ÷ 16 3 tenths x 16 = 48 60 tenths – 48 tenths There are 12 tenths left over. Divide the hundredths 128 ÷ 16 8 hundredths x 16 128 – 128 = 0 There are 0 hundredths left over. So, 6.08 ÷ 16 = 0.38

Question 11. 7.45 ÷ 5 = _______ Answer: Divide the tenths 74 ÷ 5 14 tenths x 5 = 70 74 tenths – 70 tenths There are 4 tenths left over. Divide the hundredths 45 ÷ 5 9 hundredths x 5 = 45 45 – 45 = 0 There are 0 hundredths left over. So, 7.45 ÷ 5 = 1.49

Question 12. 147.63 ÷ 37 = _______ Answer: Divide the ones 147 ÷ 37 3 ones x 37 = 111 147 ones – 111 ones There are 36 ones left over. Divide the tenths 366 ÷ 37 9 tenths x 37 = 333 366 – 333 = 33 Divide the hundredths 333 ÷ 37 = 9 hundredths So, 147.63 ÷ 37 = 3.99

Find the value of y.

Question 13. y ÷ 44 = 1.82 Answer: y = 44 x 1.82 y = 80.08

Question 14. 106.6 ÷ 82 = y Answer: Divide the ones 106 ÷ 82 1 ones x 82 = 82 106 ones – 82 ones There are 24 ones left over. Divide the tenths 246 ÷ 82 3 tenths x 82 = 246 246 – 246 = 0 106.6 ÷ 82 = 1.3, y = 1.3

Question 15. y ÷ 13 = 2.6 Answer: y = 13 x 2.6 y = 33.8

Dividend is 20 and divisor is 12 .

Question 18. Descartes borrows $6,314.76 for an all-terrain vehicle. He pays back the money in equal amounts each month for 3 years. What is his monthly payment? Answer: Time t = 3 years = 3 x 12 = 36 months Descartes borrowed amount = $6,314.76 6,314.76 ÷ 36 63 ÷ 36 = 1 and 27 is left over 271 ÷ 36 = 7 and 19 is left over 194 ÷ 36 = 5 and 14 is left over 147 ÷ 36 = 4 and 3 is left over 36 ÷ 36 = 1 and 0 left over. 6,314.76 ÷ 36 = 175.41 Descartes monthly payment is $175.41

Question 19. A blue car travels 297.6 miles using 12 gallons of gasoline and a red car travels 358.8 miles using 13 gallons of gasoline. Which car travels farther using 1 gallon of gasoline? How much farther? Answer: 297 ones ÷ 12 = 24 ones x 12 = 288 297 ones – 288 ones There are 9 ones left over. 96 ÷ 12 = 8 tenths x 12 = 96 96 – 96 = 0 There are 0 hundredths left over. So, 297.6 ÷ 12 = 24.8 358 ones ÷ 13 = 27 ones x 13 = 351 358 ones – 351 ones There are 7 ones left over. 78 ÷ 13 = 6 tenths x 13 = 78 78 – 78 = 0 There are 0 hundredths left over. So, 358.8 ÷ 13 = 27.6 Red car – blue car = 27.6 – 24.8 = 2.8 Red car travels 2.8 miles farther than blue car using 1 gallon of gasoline.

Place a decimal point where it belongs in the quotient. Question 1. 127.2 ÷ 24 = 5 . 3 Answer:

Question 2. 48.64 ÷ 32 = 1 . 5 2 Answer:

Question 3. 514.18 ÷ 47 = 1 0 . 9 4 Answer:

Find the quotient. Then check your answer. Question 4. \(\sqrt [ 72 ]{ 93.6 } \) Answer: Divide the ones 93 ÷ 72 1 ones x 72 = 72 93 ones – 72 ones There are 21 ones left over. Divide the tenths 216 ÷ 72 = 3 tenths. So, 93.6 ÷ 72 = 1.3

Question 5. \(\sqrt [ 7 ]{ 3.92 } \) Answer: Divide the tenths 39 ÷ 7 5 ones x 7 = 35 39 ones – 35 ones There are 4 ones left over. Divide the hundredths 42 ÷ 7 = 6 tenths. So, 3.92 ÷ 7 = 0.56

Question 6. \(\sqrt [ 29 ]{ 1.74 } \) Answer: Divide the hundredths 174 ÷ 29 6 ones x 29 = 174 174 hundredths – 174 hundredths There are 0 hundredths left over. So, 1.74 ÷ 29 = 0.06

Question 7. 24.3 ÷ 9 = _______ Answer: Divide the ones 24 ÷ 9 2 ones x 9 = 18 24 ones – 18 ones There are 6 ones left over. Divide the tenths 63 ÷ 9 7 tenths x 9 = 63 63 – 63 = 0 There are 0 tenths left over. So, 24.3 ÷ 9 = 2.7

Question 8. 244.9 ÷ 31 = ______ Answer: Divide the ones 244 ÷ 31 7 ones x 31 = 217 244 ones – 217 ones There are 27 ones left over. Divide the tenths 279 ÷ 31 9 tenths x 31 279 – 279 = 0 There are 0 tenths left over. So, 244.9 ÷ 31 = 7.9

Question 9. 55.62 ÷ 27 = ______ Answer: Divide the ones 55 ÷ 27 2 ones x 27 = 54 55 ones – 54 ones There is 1 ones left over. Divide the tenths 162 ÷ 27 6 tenths x 27 162 – 162 = 0 There are 0 tenths left over. So, 55.62 ÷ 27 = 2.06

Find the value of y. Question 10. y ÷ 16 = 0.23 Answer: y = 16 x 0.23 y = 3.68

Question 11. 44.1 ÷ 21 = y Answer: Divide the ones 44 ÷ 21 2 ones x 21 = 42 44 ones – 42 ones

There are 2 ones left over. Divide the tenths 21 ÷ 21 1 tenths x 21 21 – 21 = 0 There are 0 tenths left over. So, 44.1 ÷ 21 = 2.1

Question 12. y ÷ 28 = 11.04 Answer: y = 28 x 11.04 y = 309.12

Question 15. Modeling Real Life You have hip-hop dance practice for 5 weeks. You attend practice 5 days each week. Each practice is the same length of time. You practice for 37.5 hours altogether. How many hours do you practice each day? Answer: To find the total number of days you practice in 5 weeks, multiply the days you practice each week by 5. 5 × 5 = 25 So, you practice 25 days in 5 weeks. To find the number of hours you practice each day, divide the total number of hours by the number of days you practice in 5 weeks. 37.5 ÷ 25 Divide the ones 37 ÷ 25 1 ones x 25 = 25 37 ones – 25 ones There are 12 ones left over. Divide the tenths 125 ÷ 25 5 tenths x 25 125 tenths – 125 tenths There are 0 tenths left over. So, 37.5 ÷ 25 = 1.5 So, I practice dance 1.5 hours each day.

Find the product. Question 17. 0.52 × 0.4 = _______ Answer: 0.208

Question 18. 0.7 × 21.3 = _______ Answer: 14.91

Question 19. 1.52 × 8.6 = ______ Answer: 13.072

Structure When using a model to divide decimals, how do you determine the number of rows and columns to shade? How do you divide the shaded region? Answer:

Question 7. You have$1.50 in dimes. You exchange all of your dimes for quarters. How many quarters do you get? Answer: Quarter = 0.25 1.50 ÷ 0.25 Shade 15 columns to represent 1.50. Divide the model to show groups of 0.25. There are 6 groups of 25 hundredths. So, 1.50 ÷ 0.25 = 6 quarters.

Question 10. Use the table above. Is neon more than 9 times as dense as hydrogen? Answer: Divide the density of neon by the density of hydrogen to find how many times as dense it is. Use a model. Shade 9 columns to represent 0.9. Divide the model to show groups of 0.09. There are 10 groups of 9 hundredths. So, 0.9 ÷ 0.09 = 10 Compare the quotient to 9. So, neon is more than 9 times as dense as hydrogen.

Question 12. DIG DEEPER! You have 2.88 meters of copper wire and 5.85 meters of aluminum wire. You need 0.24 meter of copper wire to make one bracelet and 0.65 meter of aluminum wire to make one necklace. Can you make more bracelets or more necklaces? Explain. Answer: Copper wire = 2.88 ÷ 0.24 Shade 28.8 columns to represent 2.88. Divide the model to show groups of 0.24. There are 12 groups of 24 hundredths. So, 2.88 ÷ 0.24 = 12 Aluminum wire = 5.85 ÷ 0.65 Shade 58.5 columns to represent 5.85. Divide the model to show groups of 0.65. There are 9 groups of 65 hundredths. So, 5.85 ÷ 0.65 = 9 So, we can make more bracelets.

Question 5. You have a piece of scrapbook paper that is 1.5 feet long. You cut it into pieces that are each 0.5 foot long. How many pieces of scrap book paper do you have now? Answer: 1.5 ÷ 0.5 Shade 15 columns to represent 1.5. Divide the model to show groups of 0.5. There are 3 groups of 5 tenths. So, 1.5 ÷ 0.5 = 3 So, I have 3 pieces of scrap book paper.

Question 7. Writing Write a real-life problem that involves dividing a decimal by another decimal. Answer:

Complete the equation. Identify the property shown. Question 10. 3 × 14 = 14 × 3 Answer: Commutative Property of Multiplication

Question 11. 8 × (3 + 10) = (8 × 3) + (8 × 10) Answer: Distributive Property

Structure How can multiplying by a power of 10 help you divide decimals? Answer:

Think and Grow: Divide Decimals by Decimals

Key Idea To divide by a decimal, multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Then divide as you would with whole numbers.

Multiply the divisor by a power of 10 to make it a whole number. Then write the equivalent expression. Question 1. 3.5 ÷ 0.5 Answer: Step 1: Multiply 0.5 by a power of 10 to make it a whole number. Then multiply 3.5 by the same power of 10. 0.5 x 10 = 5 3.5 x 10 = 35 35 ÷ 5 = 7 So, 3.5 ÷ 0.5 = 7

Question 2. 9.84 ÷ 2.4 Answer: Step 1: Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 9.84 by the same power of 10. 2.4 x 10 = 24 9.84 x 10 = 98.4 Step 2: Divide 98.4 ÷ 24 98 ÷ 24 = 4 with remainder 2. 24 ÷ 24 = 1 with remainder 0. So, 9.84 ÷ 2.4 = 4.1

Question 3. 4.68 ÷ 0.78 Answer: Step 1: Multiply 0.78 by a power of 10 to make it a whole number. Then multiply 4.68 by the same power of 10. 0.78 x 100 = 78 4.68 x 100 = 468 Step 2: Divide 468 ÷ 78 = 6 So, 4.68 ÷ 0.78 = 6

Place a decimal point where it belongs in the quotient. Question 4. 28.47 ÷ 0.39 = 7 3 . 0 Answer:

Question 5. 75.85 ÷ 3.7 = 2 0 . 5 Answer:

Question 6. 4.51 ÷ 4.1 = 1 . 1 Answer:

Find the quotient. Then check your answer. Question 7. \(\sqrt [ 1.5 ]{ 7.5 } \) Answer: Step 1: Multiply 7.5 by a power of 10 to make it a whole number. Then multiply 1.5 by the same power of 10. 7.5 x 10 = 75 1.5 x 10 = 15 75 ÷ 15 = 5 So, 7.5 ÷ 1.5 = 5

Question 8. \(\sqrt [ 0.13 ]{ 0.91 } \) Answer: Step 1: Multiply 0.91 by a power of 100 to make it a whole number. Then multiply 0.13 by the same power of 100. 0.91 x 100 = 91 0.13 x 100 = 13 91 ÷ 13 = 7 So, 0.91 ÷ 0.13 = 7

Question 9. \(\sqrt [ 2.4 ]{ 2.88 } \) Answer: Step 1: Multiply 2.88 by a power of 10 to make it a whole number. Then multiply 2.4 by the same power of 10. 2.88 x 10 = 28.8 2.4 x 10 = 24 Step 2: Divide 28.8 ÷ 24 28 ÷ 24 = 1 with remainder 4. 48 ÷ 24 = 2 with remainder 0. So, 2.88 ÷ 2.4 = 1.2

Question 10. \(\sqrt [ 0.6 ]{ 7.8 } \) Answer: Step 1: Multiply 7.8 by a power of 10 to make it a whole number. Then multiply 0.6 by the same power of 10. 7.8 x 10 = 78 0.6 x 10 = 6 78 ÷ 6 = 13 So, 7.8 ÷ 0.6 = 13

Question 11. \(\sqrt [ 3.6 ]{ 4.32 } \) Answer: Step 1: Multiply 4.32 by a power of 10 to make it a whole number. Then multiply 3.6 by the same power of 10. 4.32 x 10 = 43.2 3.6 x 10 = 36 Step 2: Divide 43.2 ÷ 36 43 ÷ 36 = 1 with remainder 7. 72 ÷ 36 = 2 with remainder 0. So, 4.32 ÷ 3.6 = 1.2

Question 12. \(\sqrt [ 0.1 ]{ 11.2 } \) Answer: Step 1: Multiply 11.2 by a power of 10 to make it a whole number. Then multiply 0.1 by the same power of 10. 11.2 x 10 = 112 0.1 x 10 = 1 112 ÷ 1 = 112 So, 11.2 ÷ 0.1 = 112

Question 13. 40.42 ÷ 8.6 = ______ Answer: Step 1: Multiply 8.6 by a power of 10 to make it a whole number. Then multiply 40.42 by the same power of 10. 8.6 x 10 = 86 40.42 x 10 = 404.2 Step 2: Divide 404.2 ÷ 86 404 ÷ 86 = 4 with remainder 60. 602 ÷ 86 = 7 with remainder 0. So, 40.42 ÷ 8.6 = 4.7

Question 14. 7.2 ÷ 2.4 = _______ Answer: Step 1: Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 7.2 by the same power of 10. 2.4 x 10 = 24 7.2 x 10 = 72 Step 2: Divide 72 ÷ 24 = 3 So, 7.2 ÷ 2.4 = 3

Question 15. 5.76 ÷ 1.8 = _______ Answer: Step 1: Multiply 1.8 by a power of 10 to make it a whole number. Then multiply 5.76 by the same power of 10. 1.8 x 10 = 18 5.76 x 10 = 57.6 Step 2: Divide 57.6 ÷ 18 57 ÷ 18 = 3 with remainder 3. 36 ÷ 18 = 2 with remainder 0. So, 5.76 ÷ 1.8 = 3.2

Question 16. YOU BE THE TEACHER Descartes says 4.14 ÷ 2.3 = 1.8. Is he correct? Explain. Answer: Step 1: Multiply 2.3 by a power of 10 to make it a whole number. Then multiply 4.14 by the same power of 10. 2.3 x 10 = 23 4.14 x 10 = 41.4 Step 2: Divide 41.4 ÷ 23 41 ÷ 23 = 1 with remainder 18. 184 ÷ 23 = 8 with remainder 0. So, 4.14 ÷ 2.3 = 1.8. Descartes answer is correct.

Use the table above. Question 18. You buy a honeydew for $6.08. What is the weight of the honeydew? Answer: Honeydew price = $0.8 6.08 ÷ 0.8 Step 1: Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 6.08 by the same power of 10. 0.8 x 10 = 8 6.08 x 10 = 60.8 Step 2: Divide 60.8 ÷ 8 60 ÷ 8 = 7 with remainder 4. 48 ÷ 8 = 6 with remainder 0. So, 6.08 ÷ 0.8 = 7.6 Weight of the honeydew = 7.6 pounds

Question 19. You buy a pumpkin for $7.20 and a watermelon for $5.94. Does the watermelon or the pumpkin weigh more? How much more? Answer: Pumpkin = 7.20 ÷ 0.45 Watermelon = 5.94 ÷ 0.33 7.20 ÷ 0.45 Step 1: Multiply 0.45 by a power of 10 to make it a whole number. Then multiply 7.20 by the same power of 10. 0.45 x 100 = 45 7.20 x 100 = 720 Step 2: Divide 720 ÷ 45 = 16 Pumpkin weight = 16 pounds 5.94 ÷ 0.33 Step 1: Multiply 0.33 by a power of 10 to make it a whole number. Then multiply 5.94 by the same power of 10. 0.33 x 100 = 33 5.94 x 100 = 594 Step 2: Divide 594 ÷ 33 = 18 Watermelon weight = 18 pounds Watermelon weighs 2 pounds more than the pumpkin.

Multiply the divisor by a power of 10 to make it a whole number. Then write the equivalent expression. Question 1. 16.15 ÷ 1.9 Answer: Step 1: Multiply 1.9 by a power of 10 to make it a whole number. Then multiply 16.15 by the same power of 10. 1.9 x 10 = 19 16.15 x 10 = 161.5 Step 2: Divide 161.5 ÷ 19 161 ÷ 19 = 8 with remainder 9. 95 ÷ 19 = 5 with remainder 0. So, 16.15 ÷ 1.9 = 8.5

Question 2. 0.36 ÷ 0.09 Answer: Step 1: Multiply 0.09 by a power of 10 to make it a whole number. Then multiply 0.36 by the same power of 10. 0.09 x 100 = 9 0.36 x 100 = 36 Step 2: Divide 36 ÷ 9 = 4 So, 0.36 ÷ 0.09 = 4

Question 3. 2.04 ÷ 1.7 Answer: Step 1: Multiply 1.7 by a power of 10 to make it a whole number. Then multiply 2.04 by the same power of 10. 1.7 x 10 = 17 2.04 x 10 = 20.4 Step 2: Divide 20.4 ÷ 17 20 ÷ 17 = 1 with remainder 3. 34 ÷ 17 = 2 with remainder 0. So, 2.04 ÷ 1.7 = 1.2

Place a decimal point where it belongs in the quotient. Question 4. 81.27 ÷ 13.5 = 6 . 0 2 Answer:

Question 5. 5.76 ÷ 3.2 = 1 . 8 Answer:

Question 6. 47.15 ÷ 2.3 = 2 0 . 5 Answer:

Find the quotient. Then check your answer. Question 7. \(\sqrt [ 5.3 ]{ 21.2 } \) Answer: Step 1: Multiply 5.3 by a power of 10 to make it a whole number. Then multiply 21.2 by the same power of 10. 5.3 x 10 = 53 21.2 x 10 = 212 212 ÷ 53 = 4 So, 21.2 ÷ 5.3 = 4

Question 8. \(\sqrt [ 0.03 ]{ 76.38 } \) Answer: Step 1: Multiply 0.03 by a power of 10 to make it a whole number. Then multiply 76.38 by the same power of 10. 0.03 x 100 = 3 76.38 x 100 = 7,638 Step 2: Divide 7638 ÷ 3 76 ÷ 3 = 25 with remainder 1. 138 ÷ 3 = 46 with remainder 0. So, 76.38 ÷ 0.03 = 25.46

Question 9.

\(\sqrt [ 6.2 ]{ 33.48 } \) Answer: Step 1: Multiply 6.2 by a power of 10 to make it a whole number. Then multiply 33.48 by the same power of 10. 6.2 x 10 = 62 33.48 x 10 = 334.8 Step 2: Divide 334.8 ÷ 62 334 ÷ 62 = 5 with remainder 24. 248 ÷ 62 = 4  with remainder 0. So, 33.48 ÷ 6.2 = 5.4

Find the quotient. Then check your answer. Question 10. 0.63 ÷ 0.09 = ______ Answer: Step 1: Multiply 0.09 by a power of 10 to make it a whole number. Then multiply 0.63 by the same power of 10. 0.09 x 100 = 9 0.63 x 100 = 63 Step 2: Divide 63 ÷ 9 = 7 So, 0.63 ÷ 0.09 = 7

Question 11. 10.53 ÷ 3.9 = ______ Answer: Step 1: Multiply 3.9 by a power of 10 to make it a whole number. Then multiply 10.53 by the same power of 10. 3.9 x 10 = 39 10.53 x 10 = 105.3 Step 2: Divide 105.3 ÷ 39 105 ÷ 39 = 2 with remainder 27. 273 ÷ 39 = 7 with remainder 0. So, 10.53 ÷ 3.9 = 2.7

Question 12. 33.8 ÷ 2.6 = ______ Answer: Step 1: Multiply 2.6 by a power of 10 to make it a whole number. Then multiply 33.8 by the same power of 10. 2.6 x 10 = 26 33.8 x 10 = 338 Step 2: Divide 338 ÷ 26 = 13 So, 33.8 ÷ 2.6 = 13

Question 13. Logic Without calculating, determine whether 5.4 ÷ 0.9 is greater than or less than 5.4. Explain. Answer: 5.4 ÷ 0.9 is greater than 5.4 If the divisor is less than 1 then the quotient must be greater than the dividend.

Question 14. Structure Explain how 35.64 ÷ 2.97 compares to 3,564 ÷ 297. Answer: Both 35.64 ÷ 2.97 and 3,564 ÷ 297 are same. Both dividend and divisor are multiplied by same power of 10. 35.64 x 100 = 3564 2.97 x 100 = 297.

Question 17. Write the number in two other forms. Standard form: Word form: two hundred thirty thousand, eighty-two Expanded form: Answer: Standard form is 230,082 Expanded form is 200000 + 30000 + 80 + 2.

Reasoning Why is the number of digits in the quotients you found above different than the number of digits in the dividends? Answer:

Think and Grow: Inserting Zeros in the Dividend

Find the quotient. Then check your answer. Question 1. \(\sqrt [ 0.5 ]{ 85 } \) Answer: Multiply 0.5 by a power of 10 to make it a whole number. Then multiply 85 by the same power of 10. 0.5 x 10 = 5 85 x 10 = 850 850 ÷ 5 = 170 So, 85 ÷ 0.5 = 170.

Question 2. \(\sqrt [ 15 ]{ 9.6 } \) Answer: Insert a zero in the dividend and continue to divide. 96 ÷ 15 = 6 with remainder 6. 60 ÷ 15 = 4 with remainder 0. So, 9.6 ÷ 15 = 0.64

Question 3. \(\sqrt [ 0.24 ]{ 2.52 } \) Answer: Multiply 0.24 by a power of 10 to make it a whole number. Then multiply 2.52 by the same power of 10. 0.24 x 100 = 24 2.52 x 100 = 252 252 ÷ 24 252 ÷ 24 = 10 with remainder 12. Insert a zero in the dividend and continue to divide. 120 ÷ 24 = 5 with remainder 0. So, 2.52 ÷ 0.24 = 10.5.

Place a decimal point where it belongs in the quotient. Question 4. 3.24 ÷ 0.48 = 6 . 7 5 Answer:

Question 5. 35 ÷ 0.5 = 7 0. Answer:

Question 6. 12.8 ÷ 2.5 = 5 .1 2 Answer:

Find the quotient. Then check your answer. Question 7. \(\sqrt [ 2.4 ]{ 0.84 } \) Answer: Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 0.84 by the same power of 10. 2.4 x 10 = 24 0.84 x 10 = 8.4 Insert a zero in the dividend and continue to divide. 84 ÷ 24 = 3 with remainder 12. 120 ÷ 24 = 5 with remainder 0. So, 0.84 ÷ 2.4 = 0.35

Question 8. \(\sqrt [ 0.32 ]{ 2.08 } \) Answer: Multiply 0.32 by a power of 10 to make it a whole number. Then multiply 2.08 by the same power of 10. 0.32 x 100 = 32 2.08 x 100 = 208 208 ÷ 32 = 6 with remainder 16. Insert a zero in the dividend and continue to divide. 160 ÷ 32 = 5 with remainder 0. So, 2.08 ÷ 0.32 = 6.5

Question 9. \(\sqrt [ 4 ]{ 45.8 } \) Answer: 45.8 ÷ 4 45 ÷ 4 = 11 with remainder 1. 18 ÷ 4 = 4 with remainder 2. Insert a zero in the dividend and continue to divide. 20 ÷ 4 = 5 with remainder 0. So, 45.8 ÷ 4 = 11.45.

Question 10. 9 ÷ 1.2 = ______ Answer: Multiply 1.2 by a power of 10 to make it a whole number. Then multiply 9 by the same power of 10. 1.2 x 10 = 12 9 x 10 = 90 90 ÷ 12 Insert a zero in the dividend and continue to divide.

12 ) 90 ( 7.5

——-

0 So, 9 ÷ 1.2 = 7.5

Question 11. 3.5 ÷ 2.5 = ______ Answer: Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 3.5 by the same power of 10. 2.5 x 10 = 25 3.5 x 10 = 35 35 ÷ 25 Insert a zero in the dividend and continue to divide. 25 ) 35 ( 1.4

0 So, 3.5 ÷ 2.5 = 1.4

Question 12. 1.8 ÷ 12 = ______ Answer: Insert a zero in the dividend and continue to divide. 12 ) 18 ( 1.5

0 So, 1.8 ÷ 12 = 0.15

Answer: Total chapters in the book = 15 15 ÷ 2.5 Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 15 by the same power of 10. 2.5 x 10 = 25 15 x 10 = 150 150 ÷ 25 = 6 nights to finish the book.

Question 15. A box of 15 tablets weighs 288 ounces. Each tablet weighs the same number of ounces. What is the weight of each tablet? Answer: Divide 288 ounces by 15 to find the weight of each tablet. 288 ÷ 15

15 ) 288 ( 19.2

0 288 ÷ 15 = 19.2 The weight of each tablet = 19.2 ounces.

Question 17. DIG DEEPER! A farmer sells a pound of rice for $0.12 and a pound of oats for $0.08. Can you buy more pounds of rice or oats with $3? How much more? Explain. Answer: Rice = 3 ÷ 0.12 Multiply 0.12 by a power of 10 to make it a whole number. Then multiply 3 by the same power of 10. 0.12 x 100 = 12 3 x 100 = 300 300 ÷ 12 = 25 Oats = 3 ÷ 0.08 Multiply 0.08 by a power of 10 to make it a whole number. Then multiply 3 by the same power of 10. 0.08 x 100 = 8 3 x 100 = 300 300 ÷ 8 = 37.5 I can buy 12.5 pounds oats more than the rice.

Place a decimal point where it belongs in the quotient. Question 1. 9.3 ÷ 0.31 = 3 0. Answer:

Question 2. 10 ÷ 0.8 = 1 2 . 5 Answer:

Question 3. 0.76 ÷ 0.25 = 3 . 0 4 Answer:

Find the quotient. Then check your answer. Question 4. \(\sqrt [ 0.8 ]{ 30 } \) Answer: Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 30 by the same power of 10. 0.8 x 10 = 8 30 x 10 = 300 300 ÷ 8 30 ÷ 8 = 3 with remainder 6. 60 ÷ 8 = 7 with remainder 4. Insert a zero in the dividend and continue to divide. 40 ÷ 8 = 5 with remainder 0. So, 30 ÷ 0.8 = 37.5.

Question 5. \(\sqrt [ 15 ]{ 91.2 } \) Answer: 91.2 ÷ 15 91 ÷ 15 = 6 with remainder 1. Insert a zero in the dividend and continue to divide. 120 ÷ 15 = 8 with remainder 0. So, 91.2 ÷ 15 = 6.08

Question 6. \(\sqrt [ 35 ]{ 97.3 } \) Answer: 97.3 ÷ 35 97 ÷ 35 = 2 with remainder 27. 273 ÷ 35 = 7 with remainder 28. Insert a zero in the dividend and continue to divide. 280 ÷ 35 = 8 with remainder 0. So, 97.3 ÷ 35 = 2.78.

Question 7. 3.57 ÷ 0.84 = ______ Answer: Multiply 0.84 by a power of 10 to make it a whole number. Then multiply 3.57 by the same power of 10. 0.84 x 100 = 84 3.57 x 100 = 357 357 ÷ 84 Insert a zero in the dividend and continue to divide.

84 ) 357 ( 4.25

– 420

0 3.57 ÷ 0.84 = 4.25

Question 8. 20.2 ÷ 4 = _____ Answer: Insert a zero in the dividend and continue to divide.

4 ) 20.2 ( 5.05

——

0 20.2 ÷ 4 = 5.05

Question 9. 1.74 ÷ 0.25 = _______ Answer: Multiply 0.25 by a power of 10 to make it a whole number. Then multiply 1.74 by the same power of 10. 0.25 x 100 = 25 1.74 x 100 = 174 174 ÷ 25 Insert a zero in the dividend and continue to divide.

25 ) 174 ( 6.96

0 1.74 ÷ 0.25 = 6.96

Question 11. YOU BE THE TEACHER Your friend say she can find 5.44 ÷ 0.64 by dividing both the divisor and dividend by 0.01 to make an equivalent problem with a whole-number divisor. Is he correct? Explain. Answer: To divide this 5.44 ÷ 0.64, multiply 0.64 by a power of 10 to make it a whole number. Then multiply 5.44 by the same power of 10. Multiplying by 100 and dividing by 0.01 both are same. So, my friend is correct.

Question 12. Writing Explain when you need to insert a zero in the dividend when dividing. Answer: When dividend does not have enough digits to divide completely, then we need to insert a zero in the dividend. For example, 35 ÷ 25 Here 35 is not a multiple of 25, so we have to add a zero to 35.

Question 13. Modeling Real Life You cut a 12-foot-long streamer into 8 pieces of equal length. How long is each piece? Answer: Length of each piece = 12 ÷ 8

8 ) 12 ( 1.5

—–

0 So, length of each piece = 1.5

Find the sum. Check whether your answer is reasonable. Question 15. 1.7 + 6.8 = ________ Answer: 8.5

Question 16. 150.23 + 401.79 = _______ Answer: 552.02

Reasoning Explain how you can work backward to check your answer. Answer:

Think and Grow: Problem Solving: Decimal Operations

What do you need to find? • You need to find the cost of each video game.

Make a Plan How will you solve? Write and solve an equation to find the cost of each video game.

Question 1. Explain how you can check whether your answer above is reasonable. Answer: v = (67.45 – 15.49 – 21.99) ÷ 3 = 29.97 ÷ 3 v = 9.99 So, each video game costs $9.99.

Understand the problem. What do you know? What do you need to find? Explain. Question 2. Your friend pays $84.29 for a sewing machine and 6 yards of fabric. The sewing machine costs $59.99. How much does each yard of fabric cost? Answer:

What do you know? • You spend a total of $84.29 for a sewing machine and 6 yards of fabric. • The sewing machine costs $59.99 and the 6 yards of fabric costs $24.3.

What do you need to find?

We have to find each yard of fabric cost. 1 yard of fabric cost = 24.3 ÷ 6 So, each yard of fabric costs = $4.05

Question 3. There are 25.8 grams of fiber in 3 cups of cooked peas. There are 52.5 grams of fiber in 5 cups of avocados. Which contains more fiber in 1 cup, cooked peas or avocados? Answer: Cooked peas = 25.8 ÷ 3 = 8.6 grams Avocados = 52.5 ÷ 3 = 10.5 grams So, avocados contains more fiber in 1 cup.

Understand the problem. Then make a plan. How will you solve? Explain. Question 4. Your friend makes a hexagonal frame with a perimeter of 7.5 feet. You make a triangular frame with a perimeter of 5.25 feet. Whose frame has longer side lengths? How much longer? Answer: Hexagonal perimeter = 6a = 7.5 feet Triangular perimeter = 3sides(3a) = 5.25 feet So, 6a ÷ 2 = 3a 7.5 ÷ 2 = 3.75 feet 5.25 – 3.75 = 1.5 feet So, triangular frame has 1.5 feet longer side lengths.

Question 8. Newton buys an instant-print camera, a camera bag, and 2 packs of film. He pays $113.96 after using a $5 coupon. The camera costs $69.40, which is 5 times as much as the camera case. How much does each pack of film cost? Answer: Total cost = 113.96 + 5 = $118.96 Camera cost = $69.40 Camera case cost = 69.40 ÷ 5 = $13.88 Write and solve an equation to find the cost of each pack of film cost. cost of each pack of film = (amount spend – camera cost – camera case cost) ÷ 2 = (118.96 – 69.40 – 13.88) ÷ 2 = 35.68 ÷ 2 = 17.84 So, cost of each pack of film = $17.84

Understand the problem. What do you know? What do you need to find? Explain. Question 1. A 20-ounce bottle of ketchup costs $2.80. A 14-ounce bottle of mustard costs $2.38. Which item costs less per ounce? How much less? Answer: 20-ounce bottle of ketchup costs = $2.80 14-ounce bottle of mustard costs = $2.38 1 ounce ketchup = 2.8 ÷ 20 = $0.14 1 ounce mustard = 2.38 ÷ 14 = $0.17 Ketchup costs $0.03 less per ounce than mustard.

Understand the problem. Then make a plan. How will you solve? Explain. Question 3. Three children’s tickets to the circus cost $53.85. Two adult tickets to the circus cost $63.90. How much more does 1 adult ticket cost than 1 children’s ticket? Which item costs more per ounce? How much more? Answer: 3 children’s tickets cost = $53.85 2 adult tickets cost = $63.90 1 adult ticket cost = 63.90 ÷ 2 = $31.95 1 children’s ticket cost = 53.85 ÷ 3 = $17.95 One adult ticket cost is $14 more than 1 children’s ticket.

Question 4. A chef at a restaurant buys 50 pounds of red potatoes for $27.50 and 30 pounds of sweet potatoes for $22.50. Which kind of potato costs more per pound? How much more? Answer: Red potatoes per pound = 27.5 ÷ 50 = $0.55 Sweet potatoes per pound = 22.5 ÷ 30 = $0.75 Sweet potatoes costs $0.2 more per pound than red potatoes.

Find the quotient. Question 7. 4,000 ÷ 20 = ______ Answer: 200

Question 8. 900 ÷ 300 = _______ Answer: 3

Question 9. 5,600 ÷ 800 = _______ Answer: 7

7.1 Division Patterns with Decimals

Find the quotient. Question 1. 25 ÷ 10 2 = ______ Answer: First Simplify the 10 2 which means  10 x 10  =100, then we need to calculate the fraction to a decimal just divide the numerator (25) by the denominator (100). When we divide by 100, the decimal point moves two places to the left. 25 ÷ 10 2 = 0.25.

Question 2. 1.69 ÷ 0.01 = ______ Answer: To convert this simple fraction to a decimal just divide the numerator (1.69) by the denominator (0.01). When we divide by 0.01, the decimal point moves two places to the right.

1.69 ÷ 0.01 = 169.

Question 3. 681 ÷ 10 3 = ______ Answer: First Simplify the 10 3 which means  10 x 10 x 10 =1000, then we need to calculate the fraction to a decimal just divide the numerator (681) by the denominator (1000). When we divide by 1000, the decimal point moves three places to the left. 681 ÷ 10 3 = 0.681.

Question 4. 5.7 ÷ 0.1 = _____ Answer: To convert this simple fraction to a decimal just divide the numerator (5.7) by the denominator (0.1). When we divide by 0.1, the decimal point moves one places to the right. 5.7 ÷ 0.1 = 57

Question 5. 200 ÷ 0.01 = _____ Answer: To convert this simple fraction to a decimal just divide the numerator 200 by the denominator (0.01). When we divide by 0.01, the decimal point moves one places to the right.

Question 6. 41.3 ÷ 10 = _____ Answer: To convert this simple fraction to a decimal just divide the numerator (41.3) by the denominator (10). When we divide by 10, the decimal point moves one places to the left. 41.3 ÷ 10 = 4.13

Find the value of k. Question 7. 74 ÷ k = 7,400 Answer: 74 ÷ 7400 = k

Explanation: To convert this simple fraction to a decimal just divide the numerator (74) by the denominator (7400). When we divide by 100, the decimal point moves two places to the left. 74 ÷ 7400 = 0.01 k = 0.01.

Question 8. k ÷ 0.1 = 8.1 Answer: k = 8.1 x 0.1 k = 0.81.

Question 9. 0.35 ÷ k = 0.035 Answer: 0.35 ÷ 0.035 = k Explanation: To convert this simple fraction to a decimal just divide the numerator (0.35) by the denominator (0.035). When we divide by 0.01, the decimal point moves two places to the right. 0.35 ÷ 0.035 = 10 k = 10.

7.2 Estimate Decimal Quotients

Estimate the quotient. Question 10. 9.6 ÷ 2 Answer: 9.6 is closer to 10. 10 ÷ 2 = 5 9.6 ÷ 2 is about 5.

Question 11. 37.2 ÷ 6.4 Answer: Round the divisor 6.4 to 6. Think: What numbers close to 37.2 are easily divided by 6? Use 36. 36 ÷ 6 = 6 So, 37.2 ÷ 6.4 is about 6.

Question 12. 44.8 ÷ 4.7 Answer: Round the divisor 4.7 to 5. Think: What numbers close to 44.8 are easily divided by 5? Use 45. 45 ÷ 5 = 9 So, 44.8 ÷ 4.7 is about 9.

Question 13. 78.2 ÷ 10.8 Answer: Round the divisor 10.8 to 11. Think: What numbers close to 78.2 are easily divided by 11? Use 77. 77 ÷ 11 = 7 So, 78.2 ÷ 10.8 is about 7.

7.3 Use Models to Divide Decimals by Whole Numbers

Use a model to find the quotient. Question 16. 1.28 ÷ 4 Answer: Think: 1.28 is 1 ones, 2 tenths and 8 hundredths. 12 tenths can be divided equally as 4 groups of 3 tenths 8 hundredths can be divided equally as 4 groups of 2 hundredths . So, 128 hundredths can be divided equally as 4 groups of 32 hundredths. 1.28 ÷ 4 = 0.32

Question 17. 3.5 ÷ 5 Answer: Think: 3.5 is 3 ones and 5 tenths. 35 tenths can be divided equally as 5 groups of 7 tenths. 3.5 ÷ 5 = 0.7

7.4 Divide Decimals by One-Digit Numbers

Find the quotient. Then check your answer. Question 18. \(\sqrt [ 3 ]{ 14.1 } \) Answer: Divide the ones 14 ÷ 3 4 ones x 3 = 12 14 ones – 12 ones There are 2 ones left over. Divide the tenths 21 ÷ 3 = 7 tenths. So, 14.1 ÷ 3 = 4.7

Question 19. \(\sqrt [ 6 ]{ 67.68 } \) Answer: Divide the ones 67 ÷ 6 11 ones x 6 = 66 67 ones – 66 ones There are 1 ones left over. Divide the tenths 16 ÷ 6 2 tenths x 6 = 12 16 – 12 = 4 There are 4 tenths left over. Divide the hundredths 48 ÷ 6 = 8 hundredths. So, 67.68 ÷ 6 = 11.28

Question 20. \(\sqrt [ 8 ]{ 105.6 } \) Answer: Divide the ones 105 ÷ 8 13 ones x 8 = 104 105 ones – 104 ones There are 1 ones left over. Divide the tenths 16 ÷ 8 = 2 tenths. So, 105.6 ÷ 8 = 13.2

Question 21. Number Sense Evaluate (84.7 + 79.8) ÷ 7. Answer: (84.7 + 79.8) ÷ 7 = 164.5 ÷ 7 Divide the ones 164 ÷ 7 23 ones x 7 = 161 164 ones – 161 ones There are 3 ones left over. Divide the tenths 35 ÷ 7 5 tenths x 7 35 – 35 = 0 There are 0 tenths left over. So, 164.5 ÷ 7 = 23.5

7.5 Divide Decimals by Two-Digit Numbers

Find the quotient. Then check your answer. Question 22. \(\sqrt [ 32 ]{ 45.12 } \) Answer: Divide the ones 45 ÷ 32 1 ones x 32 = 32 45 ones – 32 ones There are 13 ones left over. Divide the tenths 131 ÷ 32 4 tenths x 32 = 128 131 – 128 = 3 There are 3 tenths left over. Divide the hundredths 32 ÷ 32 = 1 hundredths. So, 45.12 ÷ 32 = 1.41

Question 23. \(\sqrt [ 15 ]{ 9.15 } \) Answer: Divide the tenths 91 ÷ 15 6 tenths x 15 = 90 91 – 90 = 1 There are 1 tenths left over. Divide the hundredths 15 ÷ 15 = 1 hundredths. So, 9.15 ÷ 15 = 0.61

Question 24. \(\sqrt [ 73 ]{ 102.2 } \) Answer: Divide the ones 102 ÷ 73 1 ones x 73 = 73 102 ones – 73 ones There are 29 ones left over. Divide the tenths 292 ÷ 73 = 4 tenths. So, 102.2 ÷ 73 = 1.4

Question 25. 17.4 ÷ 87 = ______ Answer: Divide the tenths 174 ÷ 87 2 tenths x 87 174 – 174 = 0 There are 0 tenths left over. 17.4 ÷ 87 = 0.2

Question 26. 245.82 ÷ 51 = _______ Answer: Divide the ones 245 ÷ 51 4 ones x 51 = 204 245 ones – 204 ones There are 41 ones left over. Divide the tenths 418 ÷ 51 8 tenths x 51 418 – 408 = 10 There are 10 tenths left over. Divide the hundredths 102 ÷ 51 = 2 hundredths So, 245.82 ÷ 51 = 4.82

Question 27. 5.88 ÷ 42 = ______ Answer: Divide the tenths 58 ÷ 42 1 tenths  x 42 = 42 58 tenths – 42 tenths There are 16 tenths left over. Divide the hundredths 168 ÷ 42 4 hundredths x 42 168 – 168 = 0 There are 0 hundredths left over. So, 5.88 ÷ 42 = 0.14

7.6 Use Models to Divide Decimals

7.7 Divide Decimals

Find the quotient. Then check your answer. Question 32. \(\sqrt [ 2.57 ]{ 20.56 } \) Answer: Multiply 2.57 by a power of 10 to make it a whole number. Then multiply 20.56 by the same power of 10. 2.57 x 100 = 257 20.56 x 100 = 2056 2056 ÷ 257 = 8 So, 20.56 ÷ 2.57 = 8.

Question 33. \(\sqrt [ 4.7 ]{ 16.92 } \) Answer: Multiply 4.7 by a power of 10 to make it a whole number. Then multiply 16.92 by the same power of 10. 4.7 x 10 = 47 16.92 x 10 = 169.2 Step 2 : Divide 169.2 ÷ 47 169 ÷ 47 = 3 with remainder 28. 282 ÷ 47 = 6 with remainder 0. So, 16.92 ÷ 4.7 = 3.6.

Question 34. \(\sqrt [ 5.3 ]{ 63.6 } \) Answer: Multiply 5.3 by a power of 10 to make it a whole number. Then multiply 63.6 by the same power of 10. 5.3 x 10 = 53 63.6 x 10 = 636 636 ÷ 53 = 12 So, 63.6 ÷ 5.3 = 12.

7.8 Insert Zeros in the Dividend

Question 35. \(\sqrt [ 4 ]{ 36.2 } \) Answer: 36.2 ÷ 4 36 ÷ 4 = 9 Insert a zero in the dividend and continue to divide. 20 ÷ 4 = 5 So, 36.2 ÷ 4 = 9.05.

Question 36. \(\sqrt [ 4.8 ]{ 85.2 } \) Answer: Multiply 4.8 by a power of 10 to make it a whole number. Then multiply 85.2 by the same power of 10. 4.8 x 10 = 48 85.2 x 10 = 852 852 ÷ 48 85 ÷ 48 = 1 with remainder 37. 372 ÷ 48 = 7 with remainder 36. Insert a zero in the dividend and continue to divide. 360 ÷ 48 = 7 with remainder 24. 240 ÷ 48 = 5 with remainder 0. So, 85.2 ÷ 4.8 = 17.75.

Question 37. \(\sqrt [ 12 ]{ 52.2 } \) Answer: 52.2 ÷ 12 52 ÷ 12 = 4 with remainder 4. 42 ÷ 12 = 3 with remainder 6. Insert a zero in the dividend and continue to divide. 60 ÷ 12 = 5 with remainder 0. So, 52.2 ÷ 12 = 4.35.

Question 38. 5 ÷ 0.8 = ______ Answer: Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 5 by the same power of 10. 0.8 x 10 = 8 5 x 10 = 50 50 ÷ 8 Insert a zero in the dividend and continue to divide.

8 ) 50 ( 6.25

——–

0 So, 5 ÷ 0.8 = 6.25

Question 39. 23.7 ÷ 6 = ______ Answer: Insert a zero in the dividend and continue to divide.

6 ) 23.7 ( 3.95

0 23.7 ÷ 6 = 3.95

Question 40. 138.4 ÷ 16 = ______ Answer: Insert a zero in the dividend and continue to divide. 16 ) 138.4 ( 8.65

7.9 Problem Solving: Decimal Operations

Divide Decimals Cumulative Practice

Question 2. You round 23 × 84 and get an underestimate. How did you estimate? A. 20 × 80 B. 30 × 90 C. 25 × 90 D. 25 × 90 Answer: 23 × 84 round to 20 × 80 because it is closer to given equation. 84 is close to 80 and all the others options having number 90. Difference between the numbers in remaining options is greater than the option A numbers.

Question 5. Which number divided by 0.01 is 14 more than 37? A. 0.51 B. 5.1 C. 51 D. 5,100 Answer: 14 more than 37 = 37 + 14 = 51 51 x 0.01 = 0.51 So, the answer is 0.51 .

Question 8. What is the value of k? 0.036 × k = 36 A. 10 B. 10 3 C. 100 D. 36 Answer: k = 36 ÷ 0.036 k = 1000 = 10 3 (option B).

Question 9. What is the quotient of 11.76 and 8? A. 1.47 B. 1.97 C. 14.7 D. 94.08 Answer: 11.76 ÷ 8 11 ÷ 8 = 1 with remainder 3. 37 ÷ 8 = 4 with remainder 5. 56 ÷ 8 = 7 with remainder 0. So, quotient of 11.76 and 8 = 1.47(option A).

Question 10. Newton wins a race by seven thousandths of a second. What is this number in standard form? A. 0.007 B. 0.07 C. 0.7 D. 7,00 Answer: 0.007 is in standard form.

Question 11. Evaluate 30 – (9 + 6) ÷ 3. A. 5 B. 19 C. 9 D. 25 Answer: According to BODMAS rule. 30 – (9 + 6) ÷ 3 = 30 – (15 ÷ 3) = 30 – 5 = 25

Question 14. What is the value of b? 10 4 = 10 b × 10 A. 3 B. 4 C. 5 D. 10 Answer: 10 4 = 10 b × 10 If b= 3, 10 b × 10 = 10 3 × 10 = 10 3+1 = 10 4 So, b= 3.

Question 17. A 5-day pass to a theme park costs $72.50. A 2-day pass to the same park costs $99.50. How much more does the 2-day pass cost each day than the 5-day pass each day? A. $14.50 B. $35.25 C. $49.75 D. $64.25 Answer: 5-day pass costs each day = 72.5 ÷ 5 = $14.5 2-day pass costs each day = 99.5 ÷ 2 = $49.75 2-day pass cost each day $35.25 more than the 5-day pass each day.

Divide Decimals STEAM Performance Task

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Where Kamala Harris Stands on the Issues: Abortion, Immigration and More

She wants to protect the right to abortion nationally. Here’s what else to know about her positions.

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By Maggie Astor

• Published July 21, 2024 Updated Aug. 24, 2024

With Vice President Kamala Harris having replaced President Biden on the Democratic ticket, her stances on key issues will be scrutinized by both parties and the nation’s voters.

She has a long record in politics: as district attorney of San Francisco, as attorney general of California, as a senator, as a presidential candidate and as vice president.

Here is an overview of where she stands.

Ms. Harris supports legislation that would protect the right to abortion nationally, as Roe v. Wade did before it was overturned in 2022, in Dobbs v. Jackson Women’s Health Organization.

After the Dobbs ruling, she became central to the Biden campaign’s efforts to keep the spotlight on abortion, given that Mr. Biden — with his personal discomfort with abortion and his support for restrictions earlier in his career — was a flawed messenger. In March, she made what was believed to be the first official visit to an abortion clinic by a president or vice president.

She consistently supported abortion rights during her time in the Senate, including cosponsoring legislation that would have banned common state-level restrictions, like requiring doctors to perform specific tests or have hospital admitting privileges in order to provide abortions.

As a presidential candidate in 2019, she argued that states with a history of restricting abortion rights in violation of Roe should be subject to what is known as pre-clearance for new abortion laws — those laws would have to be federally approved before they could take effect. That proposal is not viable now that the Supreme Court has overturned Roe.

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Tracking the Atlanta Falcons 2024 Practice Squad

1) Andrew Stueber, OL

• College: Michigan
• NFL Draft History: 2022 7th Round ( New England Patriots )

A 2021 2nd Team All-American under now- Los Angeles Chargers Head Coach Jim Harbaugh, Stueber started every game at right tackle on a line of scrimmage that earned the Joe Moore Award, given yearly to the top offensive line in the nation.

2) Julién Davenport, OT

• College: Bucknell
• NFL Draft History: 2017 4th Round ( Houston Texans )

32 career NFL starts is an incredible Practice Squad member resume for Davenport and his 36.5-inch arms (34 is customarily “average”).

3) Chris Blair, X-WR

• College: Alcorn State  
• Draft: 2020 UDFA ( Green Bay Packers ) 

This 41 yard completion by Michael Penix Jr. down the sideline probably made Chris Blair feel good after his fumble. Penix’s spiral is butter 😮‍💨 pic.twitter.com/cGVNhDOOgj — Clint Goss (@NFLDraftDome) August 9, 2024

Chris Blair was one of the more obvious practice squad targets. "Been really proud of Chris Blair," Head Coach Raheem Morris said following the final preseason contest vs. the Jaguars. The production is there for Blair, having led the Falcons with eight catches and 154 receiving yards this preseason and turning in a 22.8 YPC average in the XFL in 2023. 

4) Jesse Matthews, WR

• College: San Diego State 
• Draft: 2023 UDFA (Houston Texans)

 7 REC for 57 yards this preseason was enough for historic Aztec Jesse Matthews to get a PS spot. 

5) Demone Harris, OLB

• College: Buffalo
• Draft: 2018 UDFA ( Tampa Bay Buccaneers )

One more standout on the #Texans DL for y'all - Demone Harris has shown out through two weeks. Versus the Rams he had 2 tackles, 1 sack, 1 TFL, 1 QB hit, and 3 pressures. He'll be right on that roster bubble but being able to line up on the edge and inside is a big plus. pic.twitter.com/dl7Msla8GM — Jordan Pun (@Texans_Thoughts) August 25, 2022

Super Bowl LIV Winner (KC) Demone Harris is one of the more obvious practice squad targets. With 14 NFL games played and 1 start, Harris nearly made this team.  

6) Natrone Brooks, CB

• College: Southern Miss
• Draft: 2023 UDFA ( Atlanta Falcons )

Another CB who got cut today who fits the ethos of a Dennard Wilson defense: Natrone Brooks. pic.twitter.com/efCMf4T5zH — Mike Herndon (@MikeHerndonNFL) August 27, 2024

The defensive star of the second preseason game vs. the Baltimore Ravens ? Natrone Brooks’s 13 tackles, 1 TFL, and 1 forced fumble dominated the night. A 2023 Practice Squad member, Brooks seemed to be the fan-favorite bubble player in 2024. Shifting from Ryan Nielsen’s Press-Man 4-3 scheme to Jimmy Lake’s Off-Zone 3-4 caters to a stronger year and more chances for Brooks. 

7) Dylan Drummond, WR

• College: Eastern Michigan
• Draft: 2023 UDFA ( Detroit Lions )

Dylan Drummond played in 48 games collegiately, recording 183 receptions, 2,208 yards (11.1 avg.), & 14 touchdowns. 6 catches for 22 yards in the recently completed preseason got the ex-Detroit Lions and New York Giants practice squad member a new pairing in Atlanta. 

8) Zion Logue, DT

• College: Georgia 
• Draft: 2024 6th Round (ATL)

A 2x National Champion, Zion Logue played in 50 games for Kirby Smart’s “local” Dawgs. Set for the 0/1 Tech plug of this 3-4 defense, development time is needed to improve play strength.

9) LaCale London, DT

• College: Western Illinois
• Draft: 2020 UDFA ( Chicago Bears )

LaCale London played a lot of football in 2023, appearing in seven games for the Falcons (13 tackles, 2 TFL, 1 FR) and 10 for the XFL (33 tackles, 5 TFL, 3 sacks, 2 FF, 1 FR).  

10) Kevin King, CB

• College: Washington 
• Draft: 2017 33rd Overall Pick (Green Bay Packers)

Kevin King of the @AtlantaFalcons (formerly of the @packers ) played his first NFL snaps since 2021 in the 2024 preseason opener. Four targets, no catches, one pass breakup, one interception. Not bad at all. pic.twitter.com/ywReQlnRMq — Doug Farrar ✍ (@NFL_DougFarrar) August 13, 2024

Kevin King is undoubtedly the most surprising cut for the 2024 Atlanta Falcons. The star of the Miami Dolphins game, King rose belief he could and would make the team by appearing at safety in the Game 3 loss vs. the Jacksonville Jaguars . King will see active snaps this year whether it be at safety or cornerback. The familiar (Jerry Gray and Jimmy Lake) veteran is a huge practice squad addition. 

11) Dane Cruikshank, S

• College: Arizona 
• Draft: 2018 5th Round ( Tennessee Titans )

The most underappreciated and unrecognized resume on this practice squad? Dane Cruikshank. 54 NFL games played, 4 starts, and 42 tackles over six seasons with the Chicago Bears and Tennesee Titans is welcomed to Atlanta.  A 4.41 official 40-yard dash at the NFL Combine…not bad. 

12) John Fitzpatrick, TE 

• College: Georgia
• Draft: 2022 6th Round (ATL)

Being best known for his inline blocking versus his receiving production, the addition of San Francisco’s Charlie Woerner and Ross Dwelley had John Fitzpatrick heading for the Practice Squad. 

13) Carlos Washington Jr., RB

• College: New Hampshire/Southeast Louisiana
• Draft: 2023 UDFA (ATL)

A preseason stat line of 29 rushes, 71 yards (2.4 YPC), and 1 TD for Carlos Washington Jr. was not enough to beat out 2024 6th Round pick Jase McClellan ’s of 24 rushes, 97 yards (4.0 YPC), and 1 TD for the final RB spot on the 53-man roster, but enough for another year on Atlanta’s Practice Squad. 

14) Monty Rice, LB

• Draft: 2021 3rd Round (Tennessee Titans)

Alabama-born, Rice keeps close to his parts, having played for the Tennessee Titans and the team in Louisiana. Well, it is back to Georgia like his college days as a 1st and 2nd Team All-SEC linebacker.

15) Elijah Wilkinson, OL

• College: UMass
• Draft: 2017 UDFA ( Denver Broncos )

Welcome back the big fella that helped hold down the Falcons line for nine games in 2022. Even last season he played nine more for the Arizona Cardinals, but having him on the practice squad provides a reliable potential call-up if the injury bug hits the Falcons too hard.

Clint Goss is a Falcons and NFL writer, as well as the the on-air co-host of The Falcon Fade radio show at 99.1 WDJY and lead NFL Draft Analyst for Stadium Rant. You can follow Clint actively on Twitter/X @NFLDraftDome.

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Eagles' Exec On Waiver Wire: 'It's Challenging'

John mcmullen | aug 31, 2024.

• Philadelphia Eagles

PHILADELPHIA - According to the most recent reliable estimates, about 71% of the Earth's surface is covered by water and roughly 90% of the seafloor remains uncharted.

If there’s an uncharted world in the NFL, it might be the waiver wire, a looming Boogeyman to many fans around the league who seem to always believe the rest of the league is champing at the bit to get that fourth-string defensive back who flashed for one play in the fourth quarter of a meaningless preseason game.

In truth, claiming a bunch of players off waivers – we are looking at you Carolina, and New England – is generally a very bad sign for those organizations.

This year, a whopping 26 players were claimed across the league at the initial cut down to 53, an average of 0.81 per team with the Panthers and Pats responsible for 38.% of the original claims.

What we do know about the Eagles is that vested veteran offensive lineman Nick Gates is a part of the team’s plans for Week 1 against Green Bay yet Philadelphia released the Nebraska product explaining to him that he would be elevated early in the season.

The idea behind that juggling act is that a veteran like Gates doesn’t have to go through waivers and by working out an understanding you can keep a younger player away from a potential claim.

The idea the Eagles have a better idea than anyone else about who may or may not be claimed is partially true from the perspective that the organization has the resources to do as much homework as possible.

However, in the end, it’s always just a better-educated guess.

“It’s challenging,” assistant GM Alec Halaby told Philadelphia Eagles on SI when asked about the waiver wire. “You look around the league, you try to figure out where people have a surplus, where they have deficits, where they might have some needs but that’s something that’s problematic. 

“You don’t have real certainty in any cases there where 'hey we’re going to lose this guy or we’re going to be able to get this guy back.' You learn on the fly there and you have some intuition and some instincts about it, but you can regularly be wrong.”

The Eagles claimed former San Francisco cornerback Sam Womack at the cut to 53 but so did Indianapolis and Kansas City with the Colts being awarded the player due to higher priority on the wire than a playoff team like the Eagles and the Super Bowl champions.

Philadelphia did claim defensive tackle Byron Young from Las Vegas on Thursday after the Alabama product was waived to make room for two claims the Raiders made at the initial 53, one being Indianapolis DT Jonah Laulu.

To make room for Young the Eagles waived fourth-year DT Marlon Tuipulotu, who did clear waivers before subsequently signing with the Chiefs’ practice squad.

The educated guess is that second-year CB Eli Ricks would have been on the outside, looking in had the Eagles been awarded Womack but that’s just the kind of intuition Halaby described.

Considering Carolina had top waiver priority and the Panthers claimed three cornerbacks, it seemed like a sound decision to keep Ricks on the initial 53. That said, an NFL source in Carolina told Eagles on SI Ricks was not on the Panthers’ radar.

“Some people look at it like it’s 24 hours before the deadline when these conversations are happening, but we start talking about that in late July,” Halaby said. “We’re talking about that every day, every week throughout August and then you’re trying to piece that out and sort of plan for all the eventualities and the different permeations it can take.”

MORE NFL: Eagles Name Captains, And It's The First Time Being Chosen For One Veteran

JOHN MCMULLEN

John McMullen is a veteran reporter who has covered the NFL for over two decades. The current NFL insider for JAKIB Media, John is the former NFL Editor for The Sports Network where his syndicated column was featured in over 200 outlets including the Los Angeles Times, Chicago Tribune, and Miami Herald. He was also the national NFL columnist for Today's Pigskin as well as FanRag Sports. McMullen has covered the Eagles on a daily basis since 2016, first for ESPN South Jersey and now for Eagles Today on SI.com's FanNation. You can listen to John, alongside legendary sports-talk host Jody McDonald every morning from 8-10 on ‘Birds 365,” streaming live on YouTube.com. John is also the host of his own show "Extending the Play" on AM1490 in South Jersey and part of 6ABC.com's live postgame show after every Eagles game. You can reach him at [email protected] or on Twitter @JFMcMullen

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7 5 Homework

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• Greater Than Less Than
• Measurement
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