Warm Up 8/28 Multiply the following rational numbers. 9∙ 1 3 2. 1 2 ∙ 8 11 3. 12∙ 2 3 What is the reciprocal of the following fractions? 4. 2 3 5. 5 8 6. 15 Divide the following rational numbers (Hint: Division is multiplying by the reciprocal). 7. 12÷ 1 2 8. 18÷ 3 2

Lesson 16: Applying the Properties of Operations to Multiply and Divide Rational Numbers Objectives: I can apply properties of operations as strategies to multiply and divide rational numbers by simplifying expressions.

Let’s Discuss… How can we evaluate the expression below Will different strategies result in different answers? Why or why not?

Q and A What types of strategies were used to evaluate the expressions? The strategies used were order of operations, rearranging the terms using the commutative property, and multiplying the terms in various orders using the associative property. Can you identify the benefits of choosing one strategy versus another? Multiplying the terms allowed me to combine factors in more manageable ways such as multiplying (−𝟐)×(−𝟓) to get 10. Multiplying other numbers by 10 is very easy. What is the sign of the product and how was the sign determined? The product is a positive value. Two negative values multiplied together yield a positive product. When a negative value is multiplied by a positive product, the sign of the product changes to negative again. When this negative product.

Exercise 1 – Output Side - Alone Discuss the following questions with your group: What aspects of the expression did you consider when choosing a strategy for evaluating this expression? What is the sign of the product, and how was the sign determined? How else could we have evaluated this problem?

Our Multiplication Properties Commutative Property of Multiplication Associative Property of Multiplication

Exercise 2 – Output Side - Alone Question: Is order of operations an efficient strategy to multiply the expression below? Why or why not? After students have finished: What terms did you combine first and why?

Distributive Property Example 1 Distributive Property Solve −6 ∙ 5 1 3 Rewrite the mixed number as a sum; then, multiply using the distributive property.

Exercise 3 – Output Side Solve −9∙ −3 1 2

Example 2 & 3

Reflection Questions Will different strategies result in different answers? Why or why not? How do you determine the sign of expressions that include several products and quotients? How can the properties of operations be used to multiply and divide rational numbers?

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