1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up Solve. 1. 5.2x = 127.92 x = 24.6 x t 2. = 64.2 4.1 x = 263.22
= 64.2
x = x
15.1 =
x = 39.26

3. Prep for NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
California
Standards

4. Sometimes, when solving problems, you may not need an exact answer
Sometimes, when solving problems, you may not need an exact answer. To estimate sums and differences of fractions and mixed
numbers, round each fraction to 0, , or 1. You can use a number line to help. 1 2 1 2 3 10
is closer to than to 0. 1 2 3 10

5. You can also round fractions by comparing its
numerators with its denominators.

6. Additional Example 1: Measurement Application3 5
A blue whale can grow to 33 m long, while 1 2
the great white shark may be as long as 4 m.
Estimate how much longer the blue whale is than the great white shark. 33 3 5 – 4 1 2 33 3 5 33 1 2 4 1 2 4 1 2
Round each mixed number.
= 29 – 33 1 2 4
Subtract.
The blue whale is about 29 m longer.

7. A Cocker Spaniel may grow to weigh about
Check It Out! Example 1
A Cocker Spaniel may grow to weigh about
11 kilograms while the Chihuahua may weigh about 2 kilograms. Estimate how much more the Cocker Spaniel weighs than the Chihuahua. 1 2 7 8 11 1 2 – 7 8 11 1 2 11 1 2 2 7 8
Round each mixed number. 3
= 8 – 11 1 2 3
Subtract.
The Cocker Spaniel weighs about 8 kg more. 1 2

8. Additional Example 2: Estimating Sums and Differences
Estimate each sum or difference. 7 9 2 5 A. – 7 9 2 5
1 2
Round each fraction. 1
1 2
1 2
1 – =
Subtract. 5 9 B. 4 + 3 1 8 4 5 9 4 1 2 3 1 8
Round each mixed fraction. 3 4 1 2 + 3 = 7
Add.

9. Additional Example 2: Estimating Sums and Differences
Estimate the difference. 1 8 1 12 C. – 2 2 1 8 1 12
Round each number. 2
2 – 0 = 2
Subtract.

10. Estimate each sum or difference.
Check It Out! Example 2
Estimate each sum or difference. 7 8 1 6 A. – 7 8 1 6
Round each fraction. 1
1 – 0 = 1
Subtract. 3 5 B. + 2 9 5 3
Round each mixed fraction. 5 1 2 2 9 2 5 1 2 + = 7
Add.

11. Estimate the difference.
Check It Out! Example 2
Estimate the difference. 2 9 8 15 C. 4 – 4 2 9 8 15 1 2
Round each number. 4 1 2 – = 3 4
Subtract.

12. You can estimate products and quotients of mixed numbers by rounding to the nearest whole number. If the fraction in a mixed number is greater than or equal to , round the mixed number up to the next whole number. If the fraction is less than , round down to a whole number by dropping the fraction. 1 2 1 2

13. Additional Example 3A: Estimating Products and Quotients
Estimate each product or quotient. 2 9 3 • 6 5 3 2 9 3
Round each mixed number to the nearest whole number. 6 5 7
3 • 7 = 21
Multiply.

14. Additional Example 3B: Estimating Products and Quotients
Estimate each product or quotient. 4 5 1 4
13 ÷ 2 13 4 5 14
Round each mixed number to the nearest whole number. 2 1 4 2
14 ÷ 2 = 7
Divide.

15. Estimate each product or quotient.
Check It Out! Example 3A
Estimate each product or quotient. 2 3 7 • 4 7 2 3 8
Round each mixed number to the nearest whole number. 2 3 4 3
8 • 3 = 24
Multiply.

16. Estimate each product or quotient.
Check It Out! Example 3B
Estimate each product or quotient. 7 8 1 3
11 ÷ 3 11 7 8 12
Round each mixed number to the nearest whole number. 3 1 3
12 ÷ 3 = 4
Divide.

17. Lesson Quiz
1. The new show arena being built in Franklin County is feet long and feet wide. Estimate
the difference between the length and width. 3 4 1 2
40 ft
Estimate each sum or difference. 5 9 4 5 1 2 2. + 1 2 3. 7 8 3 7 – 3 4 1 5 4. 9 – 6 4
Estimate each product or quotient. 7 8 1 6 5.
5 • 2 12 5 6 1 3 6.
17 ÷ 3 6