lesson 4 homework practice multiply integers answer key

Multiplication of Integers Exercises

Multiplying integers practice problems with answers.

Below are ten (10) practice problems that involve multiplying integers .

For your convenience, I included below the rules on how to multiply integers. In a nutshell, the product of two integers with the same sign is always positive . On the other hand, the product of two integers with different signs is always negative .

Problem 1: Multiply the integers: [latex]6 \times \left( { – 3} \right)[/latex]

[latex]-18[/latex]

Problem 2: Multiply the integers: [latex]4 \times 9[/latex]

[latex]36[/latex]

Problem 3: Multiply the integers: [latex]\left( { – 7} \right) \times \left( { – 6} \right)[/latex]

[latex]42[/latex]

Problem 4: Multiply the integers: [latex]\left( { – 5} \right) \times 12[/latex]

[latex]-60[/latex]

Problem 5: Multiply the integers: [latex]\left( { – 23} \right) \times \left( { – 1} \right)[/latex]

[latex]23[/latex]

Problem 6: Multiply the integers: [latex]\left( { – 1} \right) \times 2 \times \left( { – 3} \right)[/latex]

[latex]6[/latex]

Problem 7: Multiply the integers: [latex]5 \times 3 \times \left( { – 6} \right)[/latex]

[latex]-90[/latex]

Problem 8: Multiply the integers: [latex]\left( { – 1} \right) \times \left( { – 7} \right) \times \left( { – 8} \right)[/latex]

[latex]-56[/latex]

Problem 9: Multiply the integers: [latex]2 \times \left( { – 2} \right) \times 3 \times \left( { – 3} \right)[/latex]

Problem 10: Multiply the integers: [latex]\left( { – 4} \right) \times 6 \times \left( { – 1} \right) \times \left( { – 2} \right)[/latex]

[latex]-48[/latex]

You may also be interested in these related math lessons or tutorials:

Multiplying Integers

Chapter 2, Lesson 4: Multiplying Integers

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Math Expressions Grade 5 Unit 4 Lesson 4 Answer Key Multiply Two-Digit Numbers

Solve the questions in Math Expressions Grade 5 Homework and Remembering Answer Key Unit 4 Lesson 4 Answer Key Multiply Two-Digit Numbers to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-5-unit-4-lesson-4-answer-key/

Math Expressions Common Core Grade 5 Unit 4 Lesson 4 Answer Key Multiply Two-Digit Numbers

Math Expressions Grade 5 Unit 4 Lesson 4 Homework

Solve. Use any method.

The table shows how many newspapers are delivered each week by three paper carriers. Use the table to answer the questions. Use 1 year = 52 weeks.

Question 5. How many papers does Jameel deliver in a year? Answer: Jameel delivered 93 papers each week. 1 week = 93 papers 52 weeks = ? papers 93 x 52 = 4,836 papers Jameel deliver 4,836 papers in a year. Explanation: The above table represents the newspapers delivered each week by three paper carriers. Here 1 year is equal to 52 weeks. Multiply 52 weeks with 93 papers then the product is 4,836 papers. Jameel deliver 4,836 papers in a year.

Question 6. How many papers does Clare deliver in a year? Answer: Clare delivered 97 papers each week. 1 week = 97 papers 52 weeks = ? papers 97 x 52 = 5,044 papers Clare deliver 5,044 papers in a year. Explanation: The above table represents the newspapers delivered each week by three paper carriers. Here 1 year is equal to 52 weeks. Multiply 52 weeks with 97 papers then the product is 5,044 papers. Clare deliver 5,044 papers in a year.

Question 7. How could you find how many papers Mason delivers in a year without doing any multiplication? What is the answer? Answer: 5,044 + 52 = 5,096 papers Mason deliver 5,096 papers in a year. Explanation: The above table represents the newspapers delivered each week by three paper carriers. Here 1 year is equal to 52 weeks. Mason delivered 98 papers each week. Clare delivered 97 papers each week. So add 52 with 5,044 papers then the sum is 5,096. Mason deliver 5,096 papers in a year.

Question 8. Ray needs to know the area of his floor so he can buy the right amount of carpet. The floor is 21 feet by 17 feet. What is the area of the floor? Answer: The floor is 21 feet by 17 feet. Area of the floor = 21 feet x 17 feet = 357 square feet The area of the floor is 357 square feet. Explanation: Ray needs to know the area of his floor so he can buy the right amount of carpet. The floor is 21 feet by 17 feet. Multiply 21 feet with 17 feet the product is 357 square feet. The area of the floor is 357 square feet.

Question 9. Maria is buying flowers. Each tray of flowers costs $24. If she buys 15 trays, what will the total cost be? Answer: 1 tray of flowers = $24 15 trays of flowers = ? $ 15 X $24 = $360 The total cost of flowers is #360. Explanation: Maria is buying flowers. Each tray of flowers costs $24. She buys 15 trays. Multiply 15 tray of flowers with $24 the product is $360. The total cost of flowers is #360.

Math Expressions Grade 5 Unit 4 Lesson 4 Remember

Copy each exercise. Then subtract.

Question 1. 9,000 – 865 = ___ Answer: 9,000 – 865 = 8,135 Explanation: Perform Subtraction operation on these numbers 9,000 and 865. Subtract 865 from 9,000 the difference is 8,135.

Question 2. 105.66 – 98.53 = ____ Answer: 105.66 – 98.53 = 7.13 Explanation: Perform Subtraction operation on these decimal numbers 105.66 and 98.53. Subtract 98.53 from 105.66 the difference is 7.13.

Question 3. 45,688 – 5.65 = ____ Answer: 45,688 – 5.65 = 45,682.35 Explanation: Perform Subtraction operation on the number 45,688 and the decimal number 5.65. Subtract 5.65 from 45,688 the difference is 45,682.35.

Multiply. You do not need to simplify.

Question 4. \(\frac{5}{7} \cdot \frac{1}{3}\) = ____ Answer: (5/7) . (1/3) = (5/21) Explanation: Perform multiplication operation on the above two fractions (5/7) and (1/3). Multiply (5/7) with (1/3) the product is (5/21).

Question 5. \(\frac{3}{5} \cdot \frac{1}{5}\) = ____ Answer: (3/5) . (1/5) = (3/25) Explanation: Perform multiplication operation on the above two fractions (3/5) and (1/5). Multiply (3/5) with (1/5) the product is (3/25).

Question 6. \(\frac{1}{5} \cdot \frac{2}{7}\) = ____ Answer: (1/5) . (2/7) = (2/35) Explanation: Perform multiplication operation on the above two fractions (1/5) and (2/7). Multiply (1/5) with (2/7) the product is (2/35).

Question 7. \(\frac{2}{3} \cdot 5\) = ____ Answer: (2/3) . (5) = (10/3) Explanation: Perform multiplication operation on the above fraction (2/3) and number 5. Multiply (2/3) with (5) the product is (10/3).

Question 8. \(\frac{3}{4} \cdot \frac{3}{4}\) = ____ Answer: (3/4) . (3/4) = (9/16) Explanation: Perform multiplication operation on the above two fractions (3/4) and (3/4). Multiply (3/4) with (3/4) the product is (9/16).

Question 9. \(\frac{1}{2} \cdot \frac{5}{9}\) = ____ Answer: (1/2) . (5/9) = (5/18)  Explanation: Perform multiplication operation on the above two fractions (1/2) and (5/9). Multiply (1/2) with (5/9) the product is (5/18).

Solve the first problem with Place-Value Sections. Solve the other problems using any method you like.

Question 14.  Stretch Your Thinking How is multiplying a 1-digit number and a 2-digit number the same as, and different from, multiplying two 2-digit numbers? Answer:

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Combining Polynomials

4.1: Notice and Wonder: What Can Happen to Integers (5 minutes)

CCSS Standards

Building Towards

• HSA-APR.A.1

Routines and Materials

Instructional Routines

• Notice and Wonder

The purpose of this warm-up is to elicit the idea that integers can be combined in ways that result in integers, or in ways that do not result in integers. This will be useful when students experiment to find out which operations integers are closed under in a later activity. While students may notice and wonder many things about these images, the possible results of combining integers using each operation are the important discussion points.

Display the 4 equations for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner, followed by a whole-class discussion.

Student Facing

What do you notice? What do you wonder?

• \(7 \boldcdot 9 = 63\)
• \(7 + 9 = 16\)
• \(7 - 9 = \text-2\)
• \(\frac{7}{9} = 0.777 \ldots\)

Student Response

For access, consult one of our IM Certified Partners .

Activity Synthesis

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the equation. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.

If the difference between division and the other three operations—that is, that adding, subtracting, or multiplying integers results in other integers but the same is not true for division—does not come up during the conversation, ask students to discuss this idea.

4.2: Experimenting with Integers (15 minutes)

• MLR2: Collect and Display

The purpose of this activity is for students to experiment with performing operations on numbers to see which operations yield numbers of a different type than the ones they started with, and which ones do not. This introduces the idea of closure (although the word closure does not need to be introduced). Students do not have to find a complete mathematical proof for each statement they think is true, but they should construct an argument for it based on their observations (MP3).

Arrange students in groups of 2. Tell students that today, we’re going to see what happens to polynomials when we perform mathematical operations on them. We will start by experimenting with integers. Invite students to name some mathematical operations, and record them for all to see throughout the activity. If needed, remind students that an operation is something you can do to a number or a pair of numbers to get another number, like adding them or raising one to the power of the other.

Which of these statements are true? Give reasons in support of your answer.

• If you add two even numbers, you’ll always get an even number.
• If you subtract an even number from another even number, you’ll always get an even number.
• If you add two odd numbers, you’ll always get an odd number.
• If you subtract an odd number from another odd number, you’ll always get an odd number.
• If you multiply two even numbers, you’ll always get an even number.
• If you multiply two odd numbers, you’ll always get an odd number.
• If you multiply two integers, you’ll always get an integer.
• If you add two integers, you’ll always get an integer.
• If you subtract one integer from another, you’ll always get an integer.

Are you ready for more?

• If you add two rational numbers, you’ll always get a rational number.
• If you multiply two rational numbers, you’ll always get a rational number.
• If you divide two rational numbers, you’ll always get a rational number.

Pair groups together to briefly share one statement they agreed with and one statement they disagreed with.

After groups have shared with each other, here are some questions for discussion:

• “Was there anything that surprised you while you were thinking about each statement?” (I never noticed that adding two odd numbers always makes an even number. I wasn’t sure what could happen when two even numbers are multiplied, but now it makes sense that the result will always be even.)
• “If you have some odd numbers, what could you do to them to get an odd number? An even number?” (Multiply them. Add or subtract them.)
• “If you have some even numbers, what could you do to them to get an odd number?” (Average them, divide them by two, add 1 to their sum.)
• “If you have some integers, what could you do to them to get something that’s not an integer?” (Divide one of them by the other, average them.)

The purpose of the discussion is for students to understand that some operations on a type of number will produce numbers of that same type, but others will not. For example, performing multiplication on odd numbers always produces an odd number, but performing addition or subtraction on odd numbers will not produce an odd number. If students ask whether there is a word for this, tell them that another way to say this is “odd numbers are closed under multiplication.” If you have some odd numbers and you want to get another kind of number, you can’t do it by multiplying.

4.3: Experimenting with Polynomials (15 minutes)

• MLR8: Discussion Supports

Required Materials

• Pre-printed slips, cut from copies of the blackline master

The purpose of this activity is for students to experiment with adding, subtracting, and multiplying polynomials to see if they will always get a polynomial. As with the integers in the previous activity, it is not important for students to develop a mathematical proof of their answers, but they should find reasons to support their answers. They will share their reasons with others and critique each other’s arguments (MP3).

This is also a good opportunity to remind students of the wide variety of expressions that are polynomials. For example, the sample polynomials that students can use in their experiments include one with a square-root coefficient. Students will work more with roots in later lessons.

Tell students that they will experiment with polynomials in the same way they experimented with integers in the last activity. If needed, briefly remind students what counts as a polynomial. Here are some questions about polynomials for discussion if needed:

• “Can the variable have negative powers?” (No, whole numbers only.)
• “Is a single number like 10 a polynomial?” (Yes, the power on the variable is 0.)
• “Do the coefficients have to be integers?” (No.)

Then, display the first two questions from the task statement for all to see. After quiet think time, informally poll the class and record the total number of “yes” votes next to each question.

Arrange students in groups of 2. Assign each group 1 of the questions to focus on. Tell students that their job is to decide what the answer to their question is, and to find reasons that support their answers. Distribute a set of pre-cut slips of polynomials to each pair of students. Students can test these polynomials to see if performing their operation on them will always result in a polynomial, or they can write their own polynomials to test. When a pair thinks they know whether they’ll always get a polynomial, they should find reasons that support their answer.

Once a group has at least one argument to support their answer, partner them with another group and tell them to take turns sharing their reasoning while the other group listens and works to understand.

Monitor for students who give especially clear justifications or use clear diagrams to share during the whole-class discussion.

Here are some questions about polynomials. You and a partner will work on one of these questions.

• If you add or subtract two polynomials, will you always get a polynomial?
• If you multiply two polynomials, will you always get a polynomial?
• Try combining some polynomials to answer your question. Use the ones given by your teacher or make up your own polynomials. Keep a record of what polynomials you tried, and the results.
• When you think you have an answer to your question, explain your reasoning using equations, graphs, visuals, calculations, words, or in any way that will help others understand your reasons.

Anticipated Misconceptions

Students may mistakenly believe they have found an example that proves the answer to one of the questions is “no,” because either they did not start with two polynomials, they made mistakes in calculating, or they do not see that the result is a polynomial. They may catch errors when sharing with the other group. Misunderstandings about the definition of “polynomial” may be useful to bring up during the whole-class discussion, so not all such errors need to be corrected during the activity itself.

The main takeaway students should have from this activity is an understanding of some reasons why polynomials are closed under addition, subtraction, and multiplication. Revisit the poll questions about polynomials. Ask students to raise their hand if they think the answer is “yes,” and record the total. Invite any students who have changed their minds to say why. For each question, ask at least one previously identified pair to share their work.

Lesson Synthesis

A key idea of this lesson is that integers and polynomials are both closed under addition, subtraction, and multiplication. Students have seen that integers are not closed under division, so this is a good time for them to wonder about what happens when one polynomial is divided by another, although they will not learn how to divide polynomials until later in the unit. In this lesson, students did a lot of practice performing arithmetic on polynomials, so any efficient strategies should be highlighted. Here are some questions for discussion:

• “What is something you found out that was surprising?” (I didn’t know that adding two odd numbers would always give you an even number. I wasn’t sure if multiplying two polynomials would always make another polynomial, so I was surprised to find out that it does.)
• “What was difficult about doing arithmetic on polynomials? How did you deal with that difficulty?” (Multiplying polynomials is kind of messy. I wrote down each piece separately and circled the like terms so I could keep track of what to add.)
• “What do you think would happen if we divided one polynomial by another? Would we always get a polynomial?” (I don’t think so, because dividing integers doesn’t always give you an integer. If we divide \(x^2\) by \(x^3\) , we get \(x^{\text-1}\) , and that’s not a polynomial.)

4.4: Cool-down - Mind the Gaps (5 minutes)

Student lesson summary.

If we add two integers, subtract one from the other, or multiply them, the result is another integer. The same thing is true for polynomials: combining polynomials by adding, subtracting, or multiplying will always give us another polynomial.

For example, we can multiply \(\text-x^2 + 4.5\) and \(x^3 + 2x + \sqrt7\) to see what happens. We’ll need to use the distributive property, and there are a lot of ways to keep track of the results of distribution when we multiply polynomials. One way is to use a diagram like this:

Then we can find the product by adding all the results we filled in. This diagram tells us that the product is \(\text-x^5 + 2.5x^3 - \sqrt{7}x^2 + 9x + 4.5\sqrt7\) , which is also a polynomial even though there are square roots as coefficients! No matter what polynomials we started with, multiplying them would give us a polynomial, because we would have to multiply each part of each polynomial and then add them all together. Adding or subtracting polynomials also gives us a polynomial, because we can combine like terms.

When thinking about polynomials, it is important to remember exactly what counts as a polynomial. Any sum of terms that all have the same variable, where the variable is only raised to non-negative integer powers, is a polynomial. So some things that might not look like polynomials at first, like -34.1 or \(7.9998x\) , are polynomials.

Integers Worksheets

Welcome to the integers worksheets page at Math-Drills.com where you may have a negative experience, but in the world of integers, that's a good thing! This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers.

If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand. Banks like you to keep negative balances in your accounts, so they can charge you loads of interest. Deep sea divers spend all sorts of time in negative integer territory. There are many reasons why a knowledge of integers is helpful even if you are not going to pursue an accounting or deep sea diving career. One hugely important reason is that there are many high school mathematics topics that will rely on a strong knowledge of integers and the rules associated with them.

We've included a few hundred integers worksheets on this page to help support your students in their pursuit of knowledge. You may also want to get one of those giant integer number lines to post if you are a teacher, or print off a few of our integer number lines. You can also project them on your whiteboard or make an overhead transparency. For homeschoolers or those with only one or a few students, the paper versions should do. The other thing that we highly recommend are integer chips a.k.a. two-color counters. Read more about them below.

Most Popular Integers Worksheets this Week

Integer Resources

Coordinate graph paper can be very useful when studying integers. Coordinate geometry is a practical application of integers and can give students practice with using integers while learning another related skill. Coordinate graph paper can be found on the Graph Paper page:

Coordinate Graph Paper

Integer number lines can be used for various math activities including operations with integers, counting, comparing, ordering, etc.

• Integer Number Lines Integers Number Lines from -10 to 10 Integers Number Lines from -15 to 15 Integers Number Lines from -20 to 20 Integers Number Lines from -25 to 25 OLD Integer Number Lines

Comparing and Ordering Integers

For students who are just starting with integers, it is very helpful if they can use an integer number line to compare integers and to see how the placement of integers works. They should quickly realize that negative numbers are counter-intuitive because they are probably quite used to larger absolute values meaning larger numbers. The reverse is the case, of course, with negative numbers. Students should be able to recognize easily that a positive number is always greater than a negative number and that between two negative integers, the one with the lesser absolute value is actually the greater number. Have students practice with these integers worksheets and follow up with the close proximity comparing integers worksheets.

• Comparing Integers Worksheets Comparing Positive and Negative Integers (-9 to +9) Comparing Positive and Negative Integers (-15 to +15) Comparing Positive and Negative Integers (-25 to +25) Comparing Positive and Negative Integers (-50 to +50) Comparing Positive and Negative Integers (-99 to +99) Comparing Negative Integers (-15 to -1)

By close proximity, we mean that the integers being compared differ very little in value. Depending on the range, we have allowed various differences between the two integers being compared. In the first set where the range is -9 to 9, the difference between the two numbers is always 1. With the largest range, a difference of up to 5 is allowed. These worksheets will help students further hone their ability to visualize and conceptualize the idea of negative numbers and will serve as a foundation for all the other worksheets on this page.

• Comparing Integers in Close Proximity Comparing Positive and Negative Integers (-9 to +9) in Close Proximity Comparing Positive and Negative Integers (-15 to +15) in Close Proximity Comparing Positive and Negative Integers (-25 to +25) in Close Proximity Comparing Positive and Negative Integers (-50 to +50) in Close Proximity Comparing Positive and Negative Integers (-99 to +99) in Close Proximity
• Ordering Integers Worksheets Ordering Integers on a Number Line Ordering Integers (range -9 to 9) Ordering Integers (range -20 to 20) Ordering Integers (range -50 to 50) Ordering Integers (range -99 to 99) Ordering Integers (range -999 to 999) Ordering Negative Integers (range -9 to -1) Ordering Negative Integers (range -99 to -10) Ordering Negative Integers (range -999 to -100)

Adding and Subtracting Integers

Two-color counters are fantastic manipulatives for teaching and learning about integer addition. Two-color counters are usually plastic chips that come with yellow on one side and red on the other side. They might be available in other colors, so you'll have to substitute your own colors in the following description.

Adding with two-color counters is actually quite easy. You model the first number with a pile of chips flipped to the correct side and you also model the second number with a pile of chips flipped to the correct side; then you mash them all together, take out the zeros (if any) and behold, you have your answer! Need further elaboration? Read on!

The correct side means using red to model negative numbers and yellow to model positive numbers. You would model —5 with five red chips and 7 with seven yellow chips. Mashing them together should be straight forward although, you'll want to caution your students to be less exuberant than usual, so none of the chips get flipped. Taking out the zeros means removing as many pairs of yellow and red chips as you can. You can do this because —1 and 1 when added together equals zero (this is called the zero principle). If you remove the zeros, you don't affect the answer. The benefit of removing the zeros, however, is that you always end up with only one color and as a consequence, the answer to the integer question. If you have no chips left at the end, the answer is zero!

• Adding Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (75 Questions) ✎ Adding Integers from -12 to 12 (75 Questions) ✎ Adding Integers from -15 to 15 (75 Questions) ✎ Adding Integers from -20 to 20 (75 Questions) ✎ Adding Integers from -25 to 25 (75 Questions) ✎ Adding Integers from -50 to 50 (75 Questions) ✎ Adding Integers from -99 to 99 (75 Questions) ✎
• Adding Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Adding Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (50 Questions) ✎ Adding Integers from -12 to 12 (50 Questions) ✎ Adding Integers from -15 to 15 (50 Questions) ✎ Adding Integers from -20 to 20 (50 Questions) ✎ Adding Integers from -25 to 25 (50 Questions) ✎ Adding Integers from -50 to 50 (50 Questions) ✎ Adding Integers from -99 to 99 (50 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (Large Print; 25 Questions) ✎
• Vertically Arranged Integer Addition Worksheets 3-Digit Integer Addition (Vertically Arranged) 3-Digit Positive Plus a Negative Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Positive Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Negative Integer Addition (Vertically Arranged)

Subtracting with integer chips is a little different. Integer subtraction can be thought of as removing. To subtract with integer chips, begin by modeling the first number (the minuend) with integer chips. Next, remove the chips that would represent the second number from your pile and you will have your answer. Unfortunately, that isn't all there is to it. This works beautifully if you have enough of the right color chip to remove, but often times you don't. For example, 5 - (-5), would require five yellow chips to start and would also require the removal of five red chips, but there aren't any red chips! Thank goodness, we have the zero principle. Adding or subtracting zero (a red chip and a yellow chip) has no effect on the original number, so we could add as many zeros as we wanted to the pile, and the number would still be the same. All that is needed then is to add as many zeros (pairs of red and yellow chips) as needed until there are enough of the correct color chip to remove. In our example 5 - (-5), you would add 5 zeros, so that you could remove five red chips. You would then be left with 10 yellow chips (or +10) which is the answer to the question.

• Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (75 Questions) ✎ Subtracting Integers from -12 to 12 (75 Questions) ✎ Subtracting Integers from -15 to 15 (75 Questions) ✎ Subtracting Integers from -20 to 20 (75 Questions) ✎ Subtracting Integers from -25 to 25 (75 Questions) ✎ Subtracting Integers from -50 to 50 (75 Questions) ✎ Subtracting Integers from -99 to 99 (75 Questions) ✎
• Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (50 Questions) ✎ Subtracting Integers from -12 to 12 (50 Questions) ✎ Subtracting Integers from -15 to 15 (50 Questions) ✎ Subtracting Integers from -20 to 20 (50 Questions) ✎ Subtracting Integers from -25 to 25 (50 Questions) ✎ Subtracting Integers from -50 to 50 (50 Questions) ✎ Subtracting Integers from -99 to 99 (50 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎
• Vertically Arranged Integer Subtraction Worksheets 3-Digit Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Negative Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Negative Integer Subtraction (Vertically Arranged)

The worksheets in this section include addition and subtraction on the same page. Students will have to pay close attention to the signs and apply their knowledge of integer addition and subtraction to each question. The use of counters or number lines could be helpful to some students.

• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (75 Questions) ✎ Adding & Subtracting Integers from -10 to 10 (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-5) to (+5) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding & Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎

These worksheets include groups of questions that all result in positive or negative sums or differences. They can be used to help students see more clearly how certain integer questions end up with positive and negative results. In the case of addition of negative and positive integers, some people suggest looking for the "heavier" value to determine whether the sum will be positive of negative. More technically, it would be the integer with the greater absolute value. For example, in the question (−2) + 5, the absolute value of the positive integer is greater, so the sum will be positive.

In subtraction questions, the focus is on the subtrahend (the value being subtracted). In positive minus positive questions, if the subtrahend is greater than the minuend, the answer will be negative. In negative minus negative questions, if the subtrahend has a greater absolute value, the answer will be positive. Vice-versa for both situations. Alternatively, students can always convert subtraction questions to addition questions by changing the signs (e.g. (−5) − (−7) is the same as (−5) + 7; 3 − 5 is the same as 3 + (−5)).

• Scaffolded Integer Addition and Subtraction Positive Plus Negative Integer Addition (Scaffolded) ✎ Negative Plus Positive Integer Addition (Scaffolded) ✎ Mixed Integer Addition (Scaffolded) ✎ Positive Minus Positive Integer Subtraction (Scaffolded) ✎ Negative Minus Negative Integer Subtraction (Scaffolded) ✎

Multiplying and Dividing Integers

Multiplying integers is very similar to multiplication facts except students need to learn the rules for the negative and positive signs. In short, they are:

In words, multiplying two positives or two negatives together results in a positive product, and multiplying a negative and a positive in either order results in a negative product. So, -8 × 8, 8 × (-8), -8 × (-8) and 8 × 8 all result in an absolute value of 64, but in two cases, the answer is positive (64) and in two cases the answer is negative (-64).

Should you wish to develop some "real-world" examples of integer multiplication, it might be a stretch due to the abstract nature of negative numbers. Sure, you could come up with some scenario about owing a debt and removing the debt in previous months, but this may only result in confusion. For now students can learn the rules of multiplying integers and worry about the analogies later!

• Multiplying Integers with 100 Questions Per Page Multiplying Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Mixed Integers from -20 to 20 (100 Questions) ✎ Multiplying Mixed Integers from -50 to 50 (100 Questions) ✎
• Multiplying Integers with 50 Questions Per Page Multiplying Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (50 Questions) ✎
• Multiplying Integers with 25 Large Print Questions Per Page Multiplying Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

Luckily (for your students), the rules of dividing integers are the same as the rules for multiplying:

Dividing a positive by a positive integer or a negative by a negative integer will result in a positive integer. Dividing a negative by a positive integer or a positive by a negative integer will result in a negative integer. A good grasp of division facts and a knowledge of the rules for multiplying and dividing integers will go a long way in helping your students master integer division. Use the worksheets in this section to guide students along.

• Dividing Integers with 100 Questions Per Page Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (100 Questions) ✎
• Dividing Integers with 50 Questions Per Page Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (50 Questions) ✎
• Dividing Integers with 25 Large Print Questions Per Page Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

This section includes worksheets with both multiplying and dividing integers on the same page. As long as students know their facts and the integer rules for multiplying and dividing, their sole worry will be to pay attention to the operation signs.

• Multiplying and Dividing Integers with 100 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (100 Questions) ✎
• Multiplying and Dividing Integers with 75 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (75 Questions) ✎
• Multiplying and Dividing Integers with 50 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (50 Questions) ✎
• Multiplying and Dividing Integers with 25 Large Print Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

All Operations with Integers

In this section, the integers math worksheets include all of the operations. Students will need to pay attention to the operations and the signs and use mental math or another strategy to arrive at the correct answers. It should go without saying that students need to know their basic addition, subtraction, multiplication and division facts and rules regarding operations with integers before they should complete any of these worksheets independently. Of course, the worksheets can be used as a source of questions for lessons, tests or other learning activities.

• All Operations with Integers with 50 Questions Per Page (Some Parentheses) All operations with integers from -9 to 9 (50 Questions) ✎ All operations with integers from -12 to 12 (50 Questions) ✎ All operations with integers from -15 to 15 (50 Questions) ✎ All operations with integers from -20 to 20 (50 Questions) ✎ All operations with integers from -25 to 25 (50 Questions) ✎ All operations with integers from -50 to 50 (50 Questions) ✎ All operations with integers from -99 to 99 (50 Questions) ✎
• All Operations with Integers with 50 Questions Per Page (All Parentheses) All operations with integers from (-9) to (+9) All Parentheses (50 Questions) ✎ All operations with integers from (-12) to (+12) All Parentheses (50 Questions) ✎ All operations with integers from (-15) to (+15) All Parentheses (50 Questions) ✎ All operations with integers from (-20) to (+20) All Parentheses (50 Questions) ✎ All operations with integers from (-25) to (+25) All Parentheses (50 Questions) ✎ All operations with integers from (-50) to (+50) All Parentheses (50 Questions) ✎ All operations with integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• All Operations with Integers with 50 Questions Per Page (No Parentheses) All operations with integers from -9 to 9 No Parentheses (50 Questions) ✎ All operations with integers from -12 to 12 No Parentheses (50 Questions) ✎ All operations with integers from -15 to 15 No Parentheses (50 Questions) ✎ All operations with integers from -20 to 20 No Parentheses (50 Questions) ✎ All operations with integers from -25 to 25 No Parentheses (50 Questions) ✎ All operations with integers from -50 to 50 No Parentheses (50 Questions) ✎ All operations with integers from -99 to 99 No Parentheses (50 Questions) ✎

Order of operations with integers can be found on the Order of Operations page:

Order of Operations with Integers

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Chapter 2, Lesson 4: Multiplying Integers

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Spectrum Math Grade 7 Answer Key Online Pdf | Spectrum Math 7th Grade Answers

Download pdf of Spectrum Math 7th Grade Answer Key is available on this page. So, the students who are in search of the Spectrum Math Answer Key Online Pdf can get it here. View all the solutions with detailed explanations on our Spectrum Math Workbook Grade 7 Answer Key. The students of grade 7 can get the chapter-wise solutions from here. Refer to our Spectrum Math Grade 7 Solution Key to finish your homework in time and also to secure good marks.

Spectrum Math 7th Grade Answer Key | Spectrum Math Workbook Grade 7 Answer Key

Go through the list of the chapters provided below to get answers for all grade 7 chapters. We have Spectrum Math Grade 7 Answers for Chapters such as Adding and Subtracting Rational Numbers, Multiplying and Dividing Rational Numbers, Expressions, Equations, and Inequalities, Ratios and Proportional Relationships, Ratios and Proportional Relationships, Geometry, Statistics, Probability. Hit the links provided below to Download Spectrum Math Grade 7 Answer Key pdf to practice offline.

Spectrum Math Grade 7 Answer Key Online Chapter 1 Adding and Subtracting Rational Numbers

• Spectrum Math Grade 7 Chapter 1 Pretest
• Lesson 1.1 Understanding Absolute Value
• Lesson 1.2 Absolute Values and Integers
• Lesson 1.3 Subtraction as an Inverse Operation
• Lesson 1.4 Adding Fractions and Mixed Numbers
• Lesson 1.5 Adding Integers
• Lesson 1.6 Subtracting Integers
• Lesson 1.7 Subtracting Fractions and Mixed Numbers
• Lesson 1.8 Adding Using Mathematical Properties
• Lesson 1.9 Problem Solving
• Spectrum Math Grade 7 Chapter 1 Posttest

Spectrum Math Grade 7 Answers Chapter 2 Multiplying and Dividing Rational Numbers

• Spectrum Math Grade 7 Chapter 2 Pretest
• Lesson 2.1 Multiplying and the Distributive Property
• Lesson 2.2 Multiplying Fractions and Mixed Numbers
• Lesson 2.3 Multiplying Integers
• Lesson 2.4 Dividing Fractions and Mixed Numbers
• Lesson 2.5 Understanding Integer Division
• Lesson 2.6 Dividing Integers
• Lesson 2.7 Multiplying and Dividing Using Mathematical Properties
• Lesson 2.8 Converting Rational Numbers Using Division
• Lesson 2.9 Problem Solving
• Spectrum Math Grade 7 Chapter 2 Posttest

Spectrum Math 7th Grade Answer Key Chapter 3 Expressions, Equations, and Inequalities

• Spectrum Math Grade 7 Chapter 3 Pretest
• Lesson 3.1 Mathematical Properties & Equivalent Expressions
• Lesson 3.2 Solving Problems with Equivalent Expressions
• Lesson 3.3 Creating Expressions to Solve Problems
• Lesson 3.4 Using Variables to Solve Problems
• Lesson 3.5 Using Variables to Express Inequalities
• Spectrum Math Grade 7 Chapter 3 Posttest

Spectrum Math 7th Grade Answers Chapter 4 Ratios and Proportional Relationships

• Chapter 4 Pretest
• Lesson 4.1 Unit Rates with Fractions
• Lesson 4.2 Testing Proportional Relationships
• Lesson 4.3 Constants of Proportionality
• Lesson 4.4 Using Equations to Represent Proportion
• Lesson 4.5 Proportional Relationships on the Coordinate Plane
• Lesson 4.6 Problem Solving
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Spectrum Math Grade 7 Chapters 1-4 Mid-Test

Spectrum Math Workbook Grade 7 Answer Key Pdf Chapter 5 Geometry

• Spectrum Math Grade 7 Chapter 5 Pretest
• Lesson 5.1 Scale Drawings
• Lesson 5.2 Problem Solving
• Lesson 5.3 Drawing Geometric Shapes: Triangles
• Lesson 5.4 Cross Sections of 3-Dimensional Figures
• Lesson 5.5 Circles: Circumference
• Lesson 5.6 Circles: Area
• Lesson 5.7 Angle Relationships
• Lesson 5.8 Problem Solving
• Lesson 5.9 Area: Rectangles
• Lesson 5.10 Area: Triangles
• Lesson 5.11 Volume: Rectangular Prisms
• Lesson 5.12 Volume: Pyramids
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• Spectrum Math Grade 7 Chapter 5 Posttest

Spectrum 7th Grade Math Workbook Chapter 6 Statistics

• Spectrum Math Grade 7 Chapter 6 Pretest
• Lesson 6.1 Sampling
• Lesson 6.2 Drawing Inferences from Data
• Lesson 6.3 Reviewing Measures of Center
• Lesson 6.4 Comparing Similar Data Sets
• Lesson 6.5 Problem Solving with Data
• Spectrum Math Grade 7 Chapter 6 Posttest

Spectrum Math Grade 7 Book Free Download Chapter 7 Probability

• Spectrum Math Grade 7 Chapter 7 Pretest
• Lesson 7.1 Understanding Probability
• Lesson 7.2 Frequency Tables
• Lesson 7.3 Calculating Probability
• Lesson 7.4 Uniform Probability Models
• Lesson 7.5 Other Probability Models
• Lesson 7.6 Understanding Compound Events
• Lesson 7.7 Representing Compound Events
• Lesson 7.8 Problem Solving
• Spectrum Math Grade 7 Chapter 7 Posttest

Spectrum Math Grade 7 Chapters 1-7 Final Test

Advantages of Solving Spectrum Math Grade 7 Solution Key

There are several benefits of using the Spectrum Math Work Book Grade 7 Answer Key. We have mentioned a few of them for your knowledge. They are as shown below

• Tips and Guidelines provided on this page will support the students to learn the concepts with understanding.
• Free Spectrum Math Grade 7 Answer Key PDF makes it easy for you to prepare the concepts offline too whenever you have limited internet.
• With the help of Spectrum Math Grade 7 Solution Key, you can develop an ability to apply your growing mathematics mastery to real-life situations.
• Students in 7th Grade can solve problems easily in the exams and score better.

The details mentioned on this page regarding Spectrum Math Grade 7 Answers are prepared as per the latest syllabus. Start practicing the questions from here and test your math skills. If you have any doubts regarding the answers feel free to post the comments in the below comment section. Also, Bookmark our ccssmathanswers.com to get the latest updates on Spectrum Math Answers.

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