 # Applying the Properties of Operations to Multiply and Divide Rational Numbers

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Lesson Plans and Worksheets for Grade 7
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Examples, videos, and solutions to help Grade 7 students learn how to apply the properties of operations to multiply and divide rational numbers

### Lesson 16 Student Outcomes

• Students use properties of operations to multiply and divide rational numbers without the use of a calculator. They use the commutative and associative properties of multiplication to generate equivalent expressions. They use the distributive property of multiplication over addition to create equivalent expressions, representing the sum of two quantities with a common factor as a product, and vice-versa.
• Students recognize that any problem involving multiplication and division can be written as a problem involving only multiplication.
• Students determine the sign of an expression that contains products and quotients by checking whether the number of negative terms is even or odd.

### Lesson 16 Summary

Multiplying and dividing using strictly order of operations is not always efficient. The properties of multiplication allow us to manipulate expressions by rearranging and regrouping factors that are easier to compute. Where division is involved, we can easily rewrite division as multiplication to allow the use of these properties. The signs of expressions with products and quotients can be easily determined by checking whether the number of negative terms is even or odd.

### NYS Math Module 2 Grade 7 Lesson 16 Classwork

Example 1: Using the Commutative and Associative Properties to Efficiently Multiply Rational Numbers

a. Evaluate the expression below:
-6 × 2 × (-2) × (-5) × (-3)
b. What types of strategies were used to evaluate the expressions?
c. Can you identify the benefits of choosing one strategy versus another?
d. What is the sign of the product and how was the sign determined?

Exercise 1
Find an efficient strategy to evaluate the expression and complete the necessary work.
(-1) × (-3) × 10 × (-2) × 2

Exercise 2
Find an efficient strategy to evaluate the expression and complete the necessary work.

Exercise 3
What terms did you combine first and why?

Exercise 4
Refer to the example and exercises. Do you see an easy way to determine the sign of the product first?

Example 2: Using the Distributive Property to Multiply Rational Numbers
Rewrite the mixed number as a sum; then, multiply using the distributive property.
-6 × (5 1/3)

Exercise 5
Multiply the expression using the distributive property.
9 × (-3 1/2)

Example 3: Using the Distributive Property to Multiply Rational Numbers
Evaluate using the distributive property.
16 × (-3/8) + 16 × 1/4

Example 4: Using the Multiplicative Inverse to Rewrite Division as Multiplication
Rewrite the expression as only multiplication and evaluate.
1 ÷ 2/3 × (-8) × 3 ÷ (-1/2)

Exercise 6
4.2 × (-1/3) ÷ 1/6 × (-10)
Lesson 16 Problem Set
2. Evaluate the expressions using the distributive property.

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