Rewriting Problems with Rational Numbers Using Properties of Multiplication and Division

This lesson teaches how to rewrite problems involving rational numbers using the commutative and associative properties of multiplication and division. It reviews these properties, emphasizing that they apply only to addition and multiplication, not subtraction or division. Two examples demonstrate how to apply these properties to solve problems, including changing the order and grouping of numbers. The lesson concludes with a summary of the key concepts learned.

Which of the following properties allows you to change the order of numbers in a multiplication problem?

• Identity Property

• Associative Property

• Commutative Property

• Distributive Property

What is the result of applying the associative property to the expression 3 * (4 * 5)?

• 3 * 4 + 5

• 3 + (4 * 5)

• 3 * 4 * 5

• (3 * 4) * 5

In the expression 4 * (27 / 1 / 25), what is the first step to simplify it using properties?

• Multiply 4 by 27

• Subtract 25 from 27

• Change division to multiplication and use the reciprocal

• Add 27 and 25

When simplifying 25 * 2/5 / 1/4, what is the reciprocal of 1/4?

• 1/4

• 2/5

• 4

• 5/2

After changing the order and grouping in the expression 25 * 4 / 1 * 2/5, what is the final result?

• 50

• 40

• 100

• 20