Holt CA Course 1

4-1 Estimating with Fractions

Warm UpWarm Up

California StandardsCalifornia Standards

Lesson PresentationLesson Presentation

PreviewPreview

Holt CA Course 1

4-1 Estimating with Fractions

1. 5.2x = 127.92

2. = 64.2

3. 2.6 =

Warm UpSolve.

x = 24.6

x = 39.26

x = 263.22 x t 4.1

x 15.1

Holt CA Course 1

4-1 Estimating with Fractions

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

Holt CA Course 1

4-1 Estimating with Fractions

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.

12

12

0 1310

is closer to than to 0.12

310

Holt CA Course 1

4-1 Estimating with Fractions

You can also round fractions by comparing itsnumerators with its denominators.

Holt CA Course 1

4-1 Estimating with Fractions

Additional Example 1: Measurement ApplicationA blue whale can grow to 33 m long, while

35

the great white shark may be as long as 4 m.

12

Estimate how much longer the blue whale is than the great white shark.

3335

– 4 12

3335

3312

4 12

4 12

Round each mixed number.

Subtract.

The blue whale is about 29 m longer.

= 29–3312

4 12

Holt CA Course 1

4-1 Estimating with FractionsCheck It Out! Example 1

1112

– 2 78

1112

1112

2 78

3 Round each mixed number.

Subtract.= 8–1112

3 12

A Cocker Spaniel may grow to weigh about11 kilograms while the Chihuahua may weigh about 2 kilograms. Estimate how much more the Cocker Spaniel weighs than the Chihuahua.

78

12

The Cocker Spaniel weighs about 8 kg more.12

Holt CA Course 1

4-1 Estimating with Fractions

Estimate each sum or difference.

Additional Example 2: Estimating Sums and Differences

A. 79

– 25

1 25

1 2

1 – =

79

Round each fraction.

Add.

59

B. 4 + 3 18

4 59

4 12

318

3Round each mixed fraction.

Subtract.

4 12

+ 3 = 7 12

1 2

1 2

Holt CA Course 1

4-1 Estimating with Fractions

Estimate the difference.

Additional Example 2: Estimating Sums and Differences

Subtract.

18

C. 2 – 1 12

218

2 Round each number.

1 12 0

2 – 0 = 2

Holt CA Course 1

4-1 Estimating with Fractions

Estimate each sum or difference.

Check It Out! Example 2

A. 78

– 16

1 16

0

1 – 0 = 1

78

Round each fraction.

Add.

35

B. 5 + 2 29

5 35

5 12

229

2Round each mixed fraction.

Subtract.

5 12

+ 2 = 7 12

Holt CA Course 1

4-1 Estimating with Fractions

Estimate the difference.

Check It Out! Example 2

Subtract.

29

C. 4 – 8 15

4 29

4 Round each number.

8 15

12

12

– = 3 12 4

Holt CA Course 1

4-1 Estimating with Fractions

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.

12

12

Holt CA Course 1

4-1 Estimating with Fractions

Additional Example 3A: Estimating Products and Quotients

Estimate each product or quotient.

3 • 7 = 21 Multiply.

29

3 • 656

329

3

656

7

Round each mixed number to the nearest whole number.

Holt CA Course 1

4-1 Estimating with Fractions

Additional Example 3B: Estimating Products and Quotients

Estimate each product or quotient.

14 ÷ 2 = 7 Divide.

45

13 ÷ 2 14

13 45

14

214

2

Round each mixed number to the nearest whole number.

Holt CA Course 1

4-1 Estimating with Fractions

Check It Out! Example 3A

Estimate each product or quotient.

8 • 3 = 24 Multiply.

23

7 • 234

723

8

234

3

Round each mixed number to the nearest whole number.

Holt CA Course 1

4-1 Estimating with Fractions

Check It Out! Example 3B

Estimate each product or quotient.

12 ÷ 3 = 4 Divide.

78

11 ÷ 3 13

11 78

12

313

3

Round each mixed number to the nearest whole number.

Holt CA Course 1

4-1 Estimating with FractionsLesson Quiz

Estimate each sum or difference.

1. The new show arena being built in Franklin County is 150 feet long and 110 feet wide. Estimate

the difference between the length and width.

34

12

2. 59

+ 45

3. 78

– 37

4. 9 34

– 615

5. 5 • 2

4

40 ft

112

12

12

Estimate each product or quotient. 78

16

6. 17 ÷ 3 656

13