1. Evaluate each expression. Round to the nearest tenth if necessary.
Divide.
÷ ÷ 0.6
Evaluate each expression. Round to the nearest tenth if necessary.
÷ ÷ 0.25
5. A truck traveled miles on 4.2 gallons of gas. How many miles did the truck travel per gallon of gas?
6. In a recent year, the population of Texas was 22.5 million and the population of Nevada was 2.3 million. How many time more people lived in Texas than Nevada?
Course 1, Lesson 4-1

2. ANSWERS
1. 19
mpg
6. 9.8
Course 1, Lesson 4-1

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

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 4-1 Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

5. To estimate by: Using compatible numbers Rounding to 0, , or 1
The Number System
To estimate by:
Using compatible numbers
Rounding to 0, , or 1
Course 1, Lesson 4-1

6. Find a multiple of 4 close to 13. 12 and 4 are compatible
Step-by-Step Example 1.
Estimate × 13.
Find a multiple of 4 close to and 4 are compatible
numbers since 12 ÷ 4 = 3. 1
Use a model. 2
Divide the bar representing 12 into 4 sections. 3 3 3 3
Each section is of 12, or 3. 3
Label each section 3.
Use compatible numbers. 4
× 13 ≈ × 12
≈ 3
So, × 13 is about 3. 5
Need Another Example?

7. Need Another Example?
Estimate × 28.
Sample answer: × 30 = 6
Answer

8. Find a multiple of 5 close to 11. 10 and 5 are compatible
Step-by-Step Example 2.
Estimate of 11.
Find a multiple of 5 close to and 5 are compatible
numbers since 10 ÷ 5 = 2. 1 2
× 11 ≈ × 10
≈ 2 3
If of 10 is 2, then 4
of 10 is 2 × 2, or 4
So, × 11 is about 4 5
Need Another Example?

9. Need Another Example?
Estimate × 17.
Sample answer: × 16 = 12
Answer

10. Estimate by Rounding to 0, , or 1
The Number System
Estimate by Rounding to 0, , or 1
Words
Examples
If the numerator of a fraction between 0 and 1 is almost as large as the denominator, round up. If the numerator is much smaller than the denominator, round down.
rounds to 1; rounds to 0
Course 1, Lesson 4-1

11. Round to 0, , or 1. is about and is about 1.
Step-by-Step Example 3.
Estimate × . 1
Dots are placed at and . 2
Round to 0, , or is about and is about 1. 3 ×
× 1 4
× 1 = 5
So, × is about . 6
Need Another Example?

12. Need Another Example?
Estimate × .
Answer
Sample answer: 1 × 0 = 0

13. Place dots on the number line at and .
Step-by-Step Example 4.
Estimate × . 1 2
Place dots on the number line at and .
Round to 0, , or is about 0 and is about 1. 3 4 ×
0 × 1 =
So, × is about 5
Need Another Example?

14. Need Another Example?
Estimate × .
Answer
Sample answer: 1 × =

15. Estimate the area of the flower bed.
Step-by-Step Example 5.
Estimate the area of the flower bed.
Round each mixed number to the
nearest whole number. 1
14 × 6
15 × 6 = 90 2
So, the area is about 90 square feet. 3
Need Another Example?

16. Estimate the area of a square that has a side length of 6 inches.
Need Another Example?
Estimate the area of a square that has a side
length of 6 inches.
Sample answer: 7 in. × 7 in. or 49 in2
Answer

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?
Course 1, Lesson 4-1

18. 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 a set
Course 1, Lesson 4-1

19. Explain how you would estimate the product of and 22.
The Number System
Ratios and Proportional Relationships
Explain how you would estimate the product
of and 22.
Course 1, Lesson 4-1