Applying Properties of Operations with Rational Numbers

This lesson covers the properties of operations used to multiply and divide rational numbers without a calculator. It revisits the associative and commutative properties, previously discussed in addition and subtraction, and introduces the distributive property. The teacher provides examples and problem-solving techniques using these properties, emphasizing multiple methods to reach solutions. The lesson aims to enhance students' mathematical skills through class discussions and practical applications.

What is the main objective of this lesson?

• To solve algebraic equations

• To learn about the history of mathematics

• To demonstrate the ability to utilize properties of operations to multiply and divide rational numbers

• To use a calculator to solve problems

Which property allows you to rearrange the grouping of numbers in multiplication?

• Identity Property

• Commutative Property

• Associative Property

• Distributive Property

What does the commutative property of multiplication state?

• You can distribute a number outside the parentheses to the terms inside

• You can add zero to any number and it remains unchanged

• You can change the grouping of the numbers and the answer remains the same

• You can change the order of the numbers and the answer remains the same

In the distributive property, what do you do with the number outside the parentheses?

• Add it to the terms inside the parentheses

• Subtract it from the terms inside the parentheses

• Multiply it by each term inside the parentheses

• Divide it by each term inside the parentheses

What is the result of -6 times 16 over 3?

• 32

• 48

• -48

• -32

How can you simplify the expression 4 times -8 times 9 times 1/3 times -1/2?

• By using the commutative property

• By using the associative property

• By using the distributive property

• By using the identity property

What is the result of 4 times 4 times 3?

• 64

• 32

• 24

• 48

When adding fractions, what must be the same?

• The whole numbers

• The numerators

• The signs

• The denominators

What is the result of 16 times -1/8?

• -8

• 8

• 2

• -2

Which property allows you to change the order of numbers in multiplication without changing the result?

• Commutative Property

• Distributive Property

• Identity Property

• Associative Property