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My Math 5 Volume 1 Common Core, Grade: 5 Publisher: McGraw-Hill

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Course: 4th grade   >   Unit 5

• Estimating quotients
• Estimate quotients (3- and 4-digit divided by 1-digit)

Estimating Quotients Worksheets

How to Estimate the Outcome of Division - The division is usually thought of being the most difficult of the four basic mathematical operations. It is pretty easy to learn how to add, subtract, or even multiply. But the division is a bit more of technical operation. We need to identify first that in what number of sectors the dividend should be divided. The dividend is the number that is to be divided while the divisor is one that divides. Then comes the part of thinking whether the dividend will be evenly divided, and the answer will be a whole number or not. But before doing all of this, the answer to a division sum can also be estimated. It is pretty easy to estimate the answer to a division sum, especially one involving a larger number of digits. All you have to do is write both the dividend and the divisor as a fraction and make the dividend the numerator and the divisor as the denominator. Then divide each digit of the dividend by its corresponding digit in the divisor section. This way, you can have a really quick estimated answer to your sum. This is a quicker method of solving a division sum and getting an approximately accurate answer.

Basic Lesson

Demonstrates how to estimate quotients through the use of round estimation. Also includes practice problems. Calculate 126 ÷ 7. This can be estimated to 130/10. On dividing this, we get 13. Check this with the given problem. 13 x 7 = 91; choose a higher quotient.

Intermediate Lesson

Uses a larger more difficult numbers to round than the basic lesson.

Independent Practice 1

20 problems ask you to estimate quotients. The answers can be found below.

Independent Practice 2

20 practice problems that review estimating estimating quotients. The answers can be found below.

Homework Worksheet

12 problems to reinforce the lessons and practice pages. An example is provided.

10 problems that test quotient estimation skills.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

What's In Tap Water?

There are 104 chemical elements found in the entire universe. How many of those same chemical elements can you find in the tap water in the state of New Jersey? Approximately 98! Makes you think twice before turning on the tap now doesn't it?

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Estimating Quotients

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McGraw Hill My Math Grade 5 Chapter 4 Lesson 1 Answer Key Estimate Quotients

All the solutions provided in  McGraw Hill My Math Grade 5 Answer Key PDF Chapter 4 Lesson 1 Estimate Quotients will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 4 Lesson 1 Estimate Quotients

You can use rounding and compatible numbers to estimate quotients when dividing by two-digit divisors. By estimating first, you can determine the reasonableness of your results.

Math in My World

1. Round the divisor to the nearest ten.

Answer: Each teacher would receive about 40 fliers. Explanation: Given that, The school principal has 812 fliers to pass out equally to 19 different teachers. Now, we will find how many fliers would each teacher receive. Based on the steps, we will find them easily. So, the value is 812/19, First, round the divisor to the nearest ten. i.e., 812/20. Next, round the dividend to the nearest hundred. i.e., 800/20 Now, divide it. 800/20 = 40. So, each teacher receives 40 fliers.

2. Change the dividend to a number that is compatible with the rounded divisor, ____________. 234 → ___________

3. Divide mentally. ___________ ÷ ___________ = ___________ So, 234 ÷ 41 is about ___________ Check: Use multiplication to check your answer. ___________ × ___________ = ___________ and ___________ 234

Answer: 240 Explanation: Given that, the estimated value is 234 ÷ 41. First, round the divisor to the nearest ten. i.e., 41 nearest to ten is 40. Next, change the dividend to a number that is compatible with the rounded divisor. So, the value is 234–> 240. Now, divide it. 240 ÷ 40 = 6. So, 234 ÷ 41 is about 6. Use multiplication to check answers. 6 x 40 = 240. i.e., 240 = 234. Therefore, 234 is estimated to be 240.

Answer: No, its not possible . Only one estimation is possible for a division problem. Because in division problem, we can estimate the values to nearest tens and estimate hundreds. So, it can easily divided then no need to estimate further more. Example: He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends? There are 9 friends of seats on the bus. To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends. i.e., 9/9 = 1. He gave one apple to one friend.

Guided Practice

Question 1. Estimate 312 ÷ 31. Show how you estimated. Round the divisor to the nearest ten. 31 → ___________ Round the dividend to the nearest hundred. 312 → ___________ Divide mentally. __________ ÷ ___________ = ____________ So, 312 ÷ 31 is about ____________.

Answer: 312 ÷ 31 is about 10. Explanation: Given that, the estimated value is 312 ÷ 31. Based on the steps, we will find the value quickly. So, the value is 312 ÷ 31 First, round the divisor to the nearest ten. i.e., 312/30. Next, round the dividend to the nearest hundred. i.e., 300/30 Now, divide it. 300/30 = 10. So, 312 ÷ 31 is about 10.

Independent Practice

Estimate by rounding. Show how you estimated.

Question 2. 121 ÷ 42

Answer: 3 Explanation: Given that, the estimated value is 121 ÷ 42. Based on the steps, we will find the value easily. So, the value is 121 ÷ 42 First, round the divisor to the nearest ten. i.e.,121/40. Next, round the dividend to the nearest hundred. i.e., 120/40 Now, divide it. 120/40 = 3. So, 312 ÷ 31 is about 3.

Question 3. 400 ÷ 23

Answer: 20. Explanation: Given that, the estimated value is 400 ÷ 23. Based on the steps, we will find the value easily. So, the value is 400 ÷ 23 First, round the divisor to the nearest ten. i.e.,400/20. Next, round the dividend to the nearest hundred. i.e., 400/20 Now, divide it. 400/20 = 20. So, 400 ÷ 23 is about 20.

Question 4. 642 ÷ 83

Answer: 642÷ 83 is about 8. Explanation: Given that, the estimated value is 642÷ 83. Based on the steps, we will find the value easily. So, the value is 642÷ 83 First, round the divisor to the nearest ten. i.e.,642/80. Next, round the dividend to the nearest hundred. i.e., 640/80 Now, divide it. 640/80 = 8. So, 642 ÷ 83 is about 8.

Estimate using compatible numbers. Show how you estimated.

Question 8. 653 ÷ 52

Answer: 653÷ 52 is about 13. Explanation: Given that, the estimated value is 653÷ 52. Based on the steps, we will find the value easily. So, the value is 653÷ 52 First, round the divisor to the nearest ten. i.e.,653/50. Next, round the dividend to the nearest hundred. i.e., 650/50 Now, divide it. 650/50 = 13. So, 653 ÷ 52 is about 13.

Question 9. 208 ÷ 51

Answer: 208 ÷ 51 is about 4. Explanation: Given that, the estimated value is 208÷ 51. Based on the steps, we will find the value easily. So, the value is 208 ÷51 First, round the divisor to the nearest ten. i.e.,208/50. Next, round the dividend to the nearest hundred. i.e., 200/50 Now, divide it. 200/50 = 4. So, 200 ÷ 50 is about 4.

Question 10. 300 ÷ 59 Answer: 300÷ 59 is about 5. Explanation: Given that, the estimated value is 300÷ 59. Based on the steps, we will find the value quickly. So, the value is 300÷ 59 First, round the divisor to the nearest ten. i.e.,300/60 Next, round the dividend to the nearest hundred. i.e., 300/60    (it is already rounded to a hundred) Now, divide it. 300/60 = 5. So, 300 ÷ 60 is about 5.

Problem Solving

Question 15. The area of a rectangle is 138 square meters, and the length is 21 meters. About how many meters long is the width?

Answer: 6.57 meters long is the width. Explanation: Given that, The area of a rectangle is 138 square meters. The length is 21 meters. Now, we will find width of the rectangle. We know, the area of a rectangle formula. The formula is, Area of a rectangle is l x w. Substitute the given values in a formula. A = l x w. 138 = 21 x 3 138/21 = w W = 6.57 meters

Question 16. Mathematical PRACTICE Check for Reasonableness A box of cereal contains 340 grams of carbohydrates. If there are 12 servings, how many grams are there in one serving? Show how you estimated. Explain why your answer is reasonable.

Answer: Given that, A box of cereal contains 340 grams of carbohydrates. It servers to 12 then how many grams are there in one serving. Now, we will find the grams of one serve. So, 340 divided by 12. i.e., 340/12 = 28.3 grams. So, 28 grams are there in one serving. The answer is reasonable because the packet contains only 340 grams of cereal, we can’t increase the quantity in cereal box. So, better to serve the given quantity to 12 servings equally. Therefore, we can divide 340 into 12 parts.

HOT Problems

Question 18. Building on the Essential Question Explains when it would be useful to estimate. Answer: Estimation is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. It is very useful because it can help you to solve a problem quickly if only a rough answer is needed.

McGraw Hill My Math Grade 5 Chapter 4 Lesson 1 My Homework Answer Key

Estimate. Show how you estimated.

Question 1. 512 ÷ 52

Answer: 512÷ 52 is about 10. Explanation: Given that, the estimated value is 512÷ 52. Based on the steps, we will find the value quickly. So, the value is 512÷ 52 First, round the divisor to the nearest ten. i.e.,512/50 Next, round the dividend to the nearest hundred. i.e., 500/50 Now, divide it. 500/50 = 10. So, 512 ÷ 52 is about 10.

Question 2. 412 ÷ 97

Answer: 412÷ 97 is about 4. Explanation: Given that, the estimated value is 412÷ 97. Based on the steps, we will find the value quickly. So, the value is 412÷ 97 First, round the divisor to the nearest ten. i.e.,412/100 Next, round the dividend to the nearest hundred. i.e., 400/100 Now, divide it. 400/100 = 4. So, 412 ÷ 97 is about 4.

Question 6. A farmer has 212 acres of land for sale. He divides the land into 18 equal sections. About how many acres are in each section?

Answer: 11.7 acres are in each section. Explanation: As given in the question, the data is, A farmer has 212 acres of land for sale. He divides the land into 18 equal parts. Now, we will find how many acres are in each section. So, the values are 212 and 18. Divide 212 acres/ 18 equal parts. To get the value. i.e., 212/ 18 = 11.7 Therefore, 11.7 acres are there in each section.

Question 7. Alexander has 418 songs on his MP3 player. He divides the songs into 11 equal groups. About how many songs are in each group?

Answer: 38 songs are in each group. Explanation: Given in the question, the data is, Alexander has 418 songs on his MP3 player. He divides the songs into 11 equal groups. Now, we will find how many songs are in each section. So, the values are 418 and 11. Divide 418 songs/ 11 equal groups. To get the value. i.e., 418/ 11 = 38 Therefore, 38 songs are there in each group.

Question 8. Mathematical PRACTICE If Check for Reasonableness A restaurant ordered 833 ounces of chicken. There are 16 ounces in a pound. About how many pounds of chicken did the restaurant order?

Answer: 52 pounds of chicken did the restaurant ordered. Explanation: Given that, A restaurant ordered 833 ounces of chicken. There are 16 ounces in a pound. Now, we have to find out how many pounds of chicken did the restaurant ordered. So, the values are 833 and 16. Divide 833/ 16 i.e., 418/ 11 = 52.06 Hence, 52 pounds of chicken the restaurant will be ordered.

Test Practice

Question 9. Ms. Robbins has 600 sheets of paper for a project. She has 48 students. Which is the best estimate for the number of sheets of paper she can give to each student? (A) 10 sheets (B) 12 sheets (C) 15 sheets (D) 20 sheets

Answer: OptionB Explanation: As given in the question, Ms. Robbins has 600 sheets of paper for a project. She has 48 students. Now, find out the best estimate for the number of sheets of paper she can given to each student. So, divide 600 by 48. i.e., 600/48= 12.5 which is 12. (or) 48 is rounded to nearest to 10. i.e., 600/50 = 12. So, the best estimate for the number of sheets of paper is 12.

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