1. Multiply. Write in simplest form. 1. 2. 3. 4.
5. Half the students in an elementary school live less than 2 miles from the building. Of these, ride the bus to school. What fraction of students live less than 2 miles from the building and ride the bus to school?
Course 1, Lesson 4-3

2. ANSWERS 1. 2. 3. 4. 5.
Course 1, Lesson 4-3

3. multiply and divide fractions?
The Number System
WHAT does it mean to
multiply and divide fractions?
Course 1, Lesson 4-3

4. Mathematical Practices
The Number System
Preparation for 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
Course 1, Lesson 4-3 Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

5. To multiply fraction and a mixed number To multiply mixed numbers
The Number System
To multiply fraction and a mixed number
To multiply mixed numbers
Course 1, Lesson 4-3

6. Use compatible numbers. × 2 = 1
Step-by-Step Example 1. 1
Estimate
Use compatible numbers. × 2 = 1
Write as . 2
Multiply. 3
Simplify. Compare to the estimate. 4
Need Another Example?

7. Need Another Example?
Answer

8. Check for Reasonableness
Step-by-Step Example 2. 1
Estimate 6 2 1 3 11
Write as an improper fraction. 2 2
11 × 1
Multiply. 3
2 × 3 11 5
Simplify. 4 6 6 5
Check for Reasonableness
Need Another Example?

9. Need Another Example?
Answer

10. 3. Need Another Example? Write as . Write as . 5 5
Step-by-Step Example 3. 1
Write as Write as . 5 5
Divide 15 and 3 by their GCF, 3. 2
Then divide 10 and 8 by their GCF, 2. 4 1
Multiply the numerators and multiply the denominators. 3 4
Simplify.
Need Another Example?

11. Need Another Example?
Answer

12. There are 12 million cubic yards of concrete in the Grand Coulee Dam.
Step-by-Step Example 4.
The Hoover Dam contains 4 million cubic yards of concrete. The Grand Coulee Dam, in Washington state, contains 2 times as much concrete. How much concrete does it contain?
Estimate
4 × 3 = 12 1
Write the mixed numbers as improper fractions. 2 3 4
Divide 9 and 3 by their GCF, 3. 3
Then divide 8 and 2 by their GCF, 2. 1 1
Multiply the numerators and multiply
the denominators. 4
Simplify. 5 6
There are 12 million cubic yards of concrete in the Grand Coulee Dam.
Check for Reasonableness
12 = 12 7
Need Another Example?

13. Need Another Example?
Adriana is making banana bread for a class bake sale. The recipe calls for 1 cups of brown sugar. She is making 5 times the recipe. How much brown sugar does Adriana need?
Answer

14. Check for Reasonableness 14 ≈ 16
Step-by-Step Example 5.
Mr. Conrad’s pecan pie recipe calls for 1 cups of pecans. He plans to make 8 pies for his family reunion. How many cups of pecans will Mr. Conrad need? 1
Estimate
2 × 8 = 16
Write the mixed number as an improper fraction. Write the whole number as a fraction with a denominator of 1. 2 2
Divide 8 and 4 by their GCF, 4. 3 1
Multiply the numerators and multiply the denominators. 4
Simplify. 5 6
Check for Reasonableness
14 ≈ 16
Mr. Conrad will need 14 cups of pecans. 7
Need Another Example?

15. A recipe for chocolate chip cookies calls for 1
Need Another Example?
A recipe for chocolate chip cookies calls for 1
cups of flour. Megan needs to make 6 batches of cookies for a cookie exchange. How many cups of flour will she need?
Answer

16. How did what you learned today help you answer the
The Number System
How did what you learned
today help you answer the
WHAT does it mean to
multiply and divide fractions?
Course 1, Lesson 4-4

17. How did what you learned today help you answer the
The Number System
How did what you learned
today help you answer the
WHAT does it mean to
multiply and divide fractions?
Sample answer:
To find the portion of more than one set
To find more than one portion of more than one set
Course 1, Lesson 4-4

18. The Number System
Ratios and Proportional Relationships
Compare multiplying mixed numbers to multiplying fractions. Then write about how the previous lesson helped you to understand the concepts introduced in this lesson.
Course 1, Lesson 4-4