 # Applying the Properties of Operations to Add and Subtract Rational Numbers

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Lesson Plans and Worksheets for Grade 7
Lesson Plans and Worksheets for all Grades

Videos, examples, lessons, and solutions to help Grade 7 students learn how to apply the properties of operations to add and subtract rational numbers.

### New York State Common Core Math Module 2, Grade 7, Lesson 8 and Lesson 9

Grade 7, Module 2, Lesson 8 Worksheets (pdf)
Grade 7, Module 2, Lesson 9 Worksheets (pdf)

### Lesson 8 Outcome

• Students use properties of operations to add and subtract rational numbers without the use of a calculator.

• Students recognize that any problem involving addition and subtraction of rational numbers can be written as a problem using addition and subtraction of positive numbers only.

• Students use the commutative and associative properties of addition to rewrite numerical expressions in different forms. They know that the opposite of a sum is the sum of the opposites (e.g., -(3 + (- 4)) = -3 + 4.

### Lesson 8 Summary

• Students can use the properties of operations to add and subtract rational numbers more efficiently.

• Students learned that the opposite of a sum is the sum of its opposites.

### NYS Math Module 2 Grade 7 Lesson 8 Exercises

Example 1

Explain the meaning of “The opposite of a sum is the sum of its opposites.” Use a specific math example.

Exercise 1

Represent the following expression with a single rational number.

-2 2/5 + 3 1/4 - 3/5

Example 2

Use the number line model shown below to explain and write the opposite of 2 2/5 as a sum of two rational numbers.

Exercise 2

Rewrite each mixed number as the sum of two signed numbers.

a. - 9 5/8
b. -2 1/2
c. 8 11/12

Exercise 3

Represent each sum as a mixed number.
a. -1 + (- 5/12)
b. 30 + 1/8
c. -17 + (-1/9)

Exercise 4

Mr. Mitchell lost 10 pounds over the summer by jogging each week. By winter time, he had gained 5 1/8 pounds. Represent this situation with an expression involving signed numbers. What is the overall change in Mr. Mitchell’s weight?

Exercise 5

Jamal is completing a math problem and represents the expression -5 5/7 + 8 - 5 3/7 with a single rational number as shown in the steps below. Justify each of Jamal’s steps. Then, show another way to solve the problem.

Lesson Summary

Use the properties of operations to add and subtract rational numbers more efficiently.

The opposite of a sum is the sum of its opposites

### NYS Math Module 2 Grade 7 Lesson 8 Problem Set

6. Meghan said the opposite of the sum of 12 and 4 is 8. Do you agree? Why or why not?

7. Jolene lost her wallet at the mall. It had \$10 in it. When she got home her brother felt sorry for her and gave her \$5.75. Represent this situation with an expression involving rational numbers. What is the overall change in the amount of money Jolene has?

### NYS Math Module 2 Grade 7 Lesson 9 Exercises

Exercise 1
Unscramble the cards, and show the steps in the correct order to arrive at the solution
Examples 1 and 2
Represent each of the following expressions as one rational number. Show your steps.
Exercise 2: Team Work!
Exercise 3
Explain step by step, how to arrive at a single rational number to represent written explanation and the related math work for each step.

### NYS Math Module 2 Grade 7 Lesson 9 Problem Set

Show all steps taken to rewrite each of the following as a single rational number.
1. 80 + (-22 4/15)

3. 1/5 + 20.3 - (-5 3/5)

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