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Warm Up

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Multiply Rational Numbers

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Warm Up

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Multiply Rational Numbers

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Standards for Mathematical Content

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Multiply Rational Numbers

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7.NS.A.2.C

Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.A.3

Solve real-world and mathematical problems involving the four operations with rational numbers.

7.NS.A.1.D

Apply properties of operations as strategies to add and subtract rational numbers.

Standards for Mathematical Content

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Multiply Rational Numbers

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7.EE.B.3

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Standards for Mathematical Content

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Multiply Rational Numbers

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Standards for Mathematical Practice

MP1

Make sense of problems and persevere in solving them.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP6

Attend to precision.

MP7

Look for and make use of structure.

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Multiply Rational Numbers

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Students will apply understanding of multiplication to rational numbers, and use the order of operations to solve real-world problems.

Lesson Goal

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Multiply Rational Numbers

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The rules for integers apply to positive and negative rational numbers.

State whether the product of each expression will be positive or negative using your knowledge of multiplying integers.

Learn

Multiply Rational Numbers

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Multiply Rational Numbers

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Learn

Multiply Rational Numbers

Multiply Rational Numbers
Expression	Sign of Product
	negative
	positive
	negative
	positive

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Multiply Rational Numbers

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Example 1�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 1�Multiply Rational Numbers

	Divide by common factors.
	Multiply the numerators and denominators.
	Simplify.

McGraw Hill |

Multiply Rational Numbers

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Example 1�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 1�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 2�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 2�Multiply Rational Numbers

Think About It!

Before you begin to multiply the rational numbers, what do you need to do?

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Multiply Rational Numbers

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Example 2�Multiply Rational Numbers

	Write the mixed numbers as improper fractions.
	Divide by common factors.
	Multiply the numerators and denominators.
	Simplify.

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Multiply Rational Numbers

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Example 2�Multiply Rational Numbers

Talk About It!

How would the steps be different if you did not simplify the rational numbers before multiplying?

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Multiply Rational Numbers

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Example 2�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 2�Multiply Rational Numbers

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Multiply Rational Numbers

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Learn�Multiply Rational Numbers

When multiplying rational numbers written in different forms, write the factors in the same form.

Words	Example

If the fractions or mixed numbers are decimals that terminate, use decimals or fractions to multiply.

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Multiply Rational Numbers

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Learn�Multiply Rational Numbers

Words	Example

If the fractions or mixed numbers are decimals that repeat nonzero digits, use fractions to multiply.

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Multiply Rational Numbers

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Pause and Reflect

Create a graphic organizer that will help you understand how to determine if a fraction or mixed number is a terminating or non-terminating decimal.

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Multiply Rational Numbers

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Example 3�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 3�Multiply Rational Numbers

Think About It!

Will you write both numbers as fractions or as decimals?

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Multiply Rational Numbers

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Example 3�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 3�Multiply Rational Numbers

	Write the expression.


	Multiply the numerators and denominators.
	Simplify.

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Multiply Rational Numbers

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Example 3�Multiply Rational Numbers

Talk About It!

Is it possible to find the product without writing the numbers in the same form? Explain.

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Multiply Rational Numbers

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Example 3�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 3�Multiply Rational Numbers

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Multiply Rational Numbers

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Pause and Reflect

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Multiply Rational Numbers

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Example 4�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 4�Multiply Rational Numbers



	Divide by common factors.

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Multiply Rational Numbers

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Example 4�Multiply Rational Numbers

	Multiply the numerators and denominators.
	Simplify.

McGraw Hill |

Multiply Rational Numbers

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Example 4�Multiply Rational Numbers

McGraw Hill |

Multiply Rational Numbers

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Example 4�Multiply Rational Numbers

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Multiply Rational Numbers

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Pause and Reflect

When multiplying rational numbers, why is it beneficial to divide by common factors?

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Multiply Rational Numbers

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Example 5�Multiply Rational Numbers

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Multiply Rational Numbers

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Example 5�Multiply Rational Numbers

Think About It!

What is the sign of the product of the four numbers?

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Multiply Rational Numbers

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Example 5�Multiply Rational Numbers

Simplify.

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Multiply Rational Numbers

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Example 5�Multiply Rational Numbers

Talk About It!

How would your answer compare if you had multiplied using fractions rather than decimals?

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Multiply Rational Numbers

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Example 5�Multiply Rational Numbers

McGraw Hill |

Multiply Rational Numbers

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Example 5�Multiply Rational Numbers

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Multiply Rational Numbers

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Pause and Reflect

How can you use estimation to check your work?

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Multiply Rational Numbers

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Apply

Temperature

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Multiply Rational Numbers

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Talk About It!

Is the final temperature warmer or colder than the original temperature? Explain.

Apply

Temperature

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Multiply Rational Numbers

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Apply

Temperature

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Multiply Rational Numbers

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Apply

Temperature

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Multiply Rational Numbers

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Exit Ticket

Have you ever used a recipe to make your favorite dish? The recipe shown serves six people. You are hosting a picnic with �15 people attending.

Broccoli Pasta Salad (serves 6)
Ingredient	Amount (c)
Broccoli
Cooked Pasta
Salad Dressing
Tomatoes
Cheese
Olives

McGraw Hill |

Multiply Rational Numbers

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Exit Ticket

If you want to triple the recipe, explain how to find the amount of cooked pasta you will need.

Broccoli Pasta Salad (serves 6)
Ingredient	Amount (c)
Broccoli
Cooked Pasta
Salad Dressing
Tomatoes
Cheese
Olives

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Multiply Rational Numbers

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51 of 52

Exit Ticket

Have you ever used a recipe to make your favorite dish? The recipe shown serves six people. You are hosting a picnic with �15 people attending.

Broccoli Pasta Salad (serves 6)
Ingredient	Amount (c)
Broccoli
Cooked Pasta
Salad Dressing
Tomatoes
Cheese
Olives

McGraw Hill |

Multiply Rational Numbers

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52 of 52

Exit Ticket

If you want to triple the recipe, explain how to find the amount of cooked pasta you will need.

Broccoli Pasta Salad (serves 6)
Ingredient	Amount (c)
Broccoli
Cooked Pasta
Salad Dressing
Tomatoes
Cheese
Olives

McGraw Hill |

Multiply Rational Numbers

This material may be reproduced for licensed classroom use only and may not be further reproduced or distributed.