3-7 Estimating with Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the...

3-7 Estimating with Fractions

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


1. 5.2x = 127.92

2. = 64.2

3. 2.6 =

Warm UpSolve.

x = 24.6

x = 39.26

x = 263.22 x4.1

x 15.1


Problem of the DayFill in the square using the numbers 5–13 so that all sums (rows, columns, and main diagonals) are the same.

8 13 6

7 9 11

12 5 10


Prep for MA.7.A.3.2 Add, subtract, multiply, and divide…fractions…including solving problems in everyday contexts.Review of MA.5.A.2.2

Sunshine State Standards


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

0 125

25 is closer to than to 0.1

2


You can also round fractions by comparingnumerators with denominators.

3-7 Estimating with Fractions Additional Example 1: Measurement Application

A 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 1

2333

5 3312 4 1

2 4 12

Round each mixednumber.Subtract.

The blue whale is about 29 m longer.

= 29–3312 4 1

2Round to , round to , and round to 1.

Helpful Hint35

12

13

12

34

3-7 Estimating with FractionsCheck It Out: Example 1

1112 – 2 7

8111

2 1112 2 7

8 3 Round the mixednumber.

Subtract.= 8–1112 3 1

2

A Cocker Spaniel may grow to weigh about 11 kilograms while the Chihuahua will not weigh more than 2 kilograms. Estimate how much more the Cocker Spaniel weighs than the Chihuahua.

78

12

The Cocker Spaniel weighs about 8 kg more.12


Estimate each sum or difference.Additional Example 2: Estimating Sums and Differences

A. 79 – 2

5

1 25

1 2

1 – =

79 Round each fraction.

Add.

59B. 4 + 3 1

84 5

9 4 12

318 3 Round each mixed number.

Subtract.

4 12 + 3 = 7 1

2

1 2

1 2


Estimate the sum.Additional Example 2: Estimating Sums and Differences

Add.

18C. –2 + 7

12

–218 –2 Round each number. 7

1212

12+ = –11

2–2


Estimate each sum or difference.

Check It Out: Example 2

A. 78 – 1

6

1 16 0

1 – 0 = 1

78 Round each fraction.

Add.

35B. 5 + 2 2

95 3

5 5 12

229 2 Round each mixed number.

Subtract.

5 12 + 2 = 7 1

2


Estimate the sum.

Check It Out: Example 2

Add.

29C. –4 + 8

15

–429 –4 Round each number. 8

1512

12+ = –31

2–4


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 , you can round the mixed number up to the next whole number. If the fraction is less than , you can round down to a whole number by dropping the fraction.

12

12


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.


Additional Example 3B: Estimating Products and Quotients Estimate each product or quotient.

14 ÷ 2 = 7 Divide.

4513 ÷ 2 1

413 4

5 14

214 2


3-7 Estimating with FractionsCheck It Out: Example 3A

Estimate each product or quotient.

8 • 3 = 24 Multiply.

23

7 • 234

723 8

234 3


3-7 Estimating with FractionsCheck It Out: Example 3B

Estimate each product or quotient.

12 ÷ 3 = 4 Divide.

7811 ÷ 3 1

311 7

8 12

313 3



Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

3-7 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+ 4

5 3. 78 – 3

7

4. 9 34 – 6 1

5

5. 5 • 2

4

40 ft

112

12

12Estimate each product or quotient.

78

16

6. 17 ÷ 3 656

13


1. There are two buildings beside a park. Thefirst building is 166 ft tall, and the secondbuilding is 114 ft tall. Estimate the difference between the heights of the buildings.

A. 42 feetB. 45 feetC. 52 feetD. 55 feet


783

4


2. Estimate the sum. +

A. C. 1

B. 1 D. 2


3 4

1 2

3 4

6 7

3 5


3. Estimate the difference.8 – 5

A. 5B. 4C. 3D. 2


1 4

1 6


4. Estimate the product.5 • 3

A. 17B. 18C. 19D. 20


1 9

4 5


5. Estimate the quotient.15 ÷ 2

A. 8B. 7C. 6D. 5


3 4

1 8

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