Multiplying a Fraction and a Whole Number

Name

Reteaching

8-1

Find 12 3 _14 .

Find _35 of 15, or _35 3 15.

12 3 _14 is the same as dividing

15 4 5 5 3, so _15 3 15 5 3

12 by 4.

Since _35 is 3 times _15,

12 4 4 5 3

3

_

5

3

_

5

12 3 _14 5 3

3 15 5 3 3 __15 3 15+ 5 3 3 3 5 9.

3 15 5 9

Find each product.

1. _45 3 20 5

16

4. _25 of 15 5

6

2. _67 of 14 5

5. 400 3 _38 5

12

150

3. 24 3 _34 5

18

7 of 80 5

6. __

10

56

7. Reasoning Can you use division and mental math to find _23 of 24?

Why or why not?

Yes, because 3 is the greatest common factor

of 3 and 24. _23 of 24 5 16

The chart shows the average high temperatures for different months in Phoenix, Arizona.

Phoenix Weather

Month

Average High

February

70¡ãF

May

93¡ãF

July

105¡ãF

8. What is _45 the average temperature in July?

84¡ãF

9. What is _12 the average temperature in February?

35¡ãF

10. What is _23 the average temperature in May?

18

Topic 8

62¡ãF

? Pearson Education, Inc. 6

Reteaching 8-1

Multiplying a Fraction

and a Whole Number

Name

Practice

8-1

Multiplying a Fraction

and a Whole Number

Find each product.

12

4. _18 of 72 

9

2. _56  30 

25

600

5. 900  _23 

3. 42  _56 

35

13 of 100 

6. __

20

65

Practice 8-1

1. _34  16 

9 of 81. Explain.

7. Reasoning Without multiplying, tell which is greater, _56 of 81 or __

10

__

5.

9 of 81 because __

9 is greater than _

10

10

6

Departure City

Pittsfield, Massachusetts

Reno, Nevada

Driving Distances

Destination City

Providence, Rhode Island

Wendover, Utah

Distance

132 mi

400 mi

8. Mike drove _13 of the distance between

Pittsfield, Massachusetts, and Providence,

Rhode Island. How far did he drive?

44 mi

9. Bimal drove _35 of the distance between

Reno, Nevada, and Wendover, Utah.

How far did he drive?

240 mi

10. Estimation How many more miles does Bimal

have to drive to get to Wendover, Utah?

160 mi

11. There are 25 students in Mr. Fitch¡¯s sixth-grade class. If _35 of the

students are girls, how many girls are in Mr. Fitch¡¯s class?

A 5 girls

B 10 girls

C 15 girls

D 20 girls

? Pearson Education, Inc. 6

12. Writing to Explain Explain how you would find the product of 36 and _23.

Write the problem as 36 ? _23 .

36 ? 3 ? 12, so _13 ? 36 ? 12.

_

2 ? 36 ? 2 ? (_

1 ? 36) ? 2 ? 12 ? 24.

3

3

Topic 8

19

Name

Reteaching

8-2

Estimating Products

When you are working with fractions and mixed numbers, you can estimate using

rounding, compatible numbers, or compatible benchmark fractions.

3  21 ¡Ö 6

__

10

Think: 20 ¡Â 10  2.

3  12 using a compatible

Estimate __

10

benchmark fraction.

3 to a compatible

3  12

__

Round __

10

10

3 is

benchmark fraction. Since __

10

?

?

1

_

close to 4 and 4 is a factor of

1  12  3

_

twelve, use _14 .

4

3  12 ¡Ö 3

__

10

Think: 12  4  3.

1  3  3.

3  2  6.

Sample answers are shown.

Estimate each product by using compatible numbers or benchmark fractions.

1. _16  19 

4. 31  _25 

7. 43  _27 

3

12

12

2.

4  10 

_

7

7  18 

5. __

12

5 

8. 35  __

12

5

9

15

3. _58  23 

9  90 

6. __

16

9. 16  _49 

15

45

8

Estimate each product by rounding each factor to the nearest whole number.

10. 6_23  5_18 ? Round 6_23:

11. 10_29  4_56 

50

7

Round 5_18:

12. 2_78  3_34 =

12

5

Multiply:

35

4 

13. 4_15  2__

10

8

14. Reasonableness Carlotta estimated that _37  20 is about _37  14  6. Is her estimate

reasonable? Why or why not?

No, a better

choice for a number compatible to

__

3

20 is 21: 7  21  9.

6  18 shown below different? Is one

15. Critical Thinking Why are the estimates of __

10

estimate better than the other?

6  18 ¡Ö __

6 ¡Á 20  12

__

10

10

6 ¡Á 18 ¡Ö _

1  18  9.

__

10

2

Sample answer: The first estimate uses a

compatible whole number to estimate and the

second uses a compatible benchmark fraction.

Both are reasonable ways to estimate, and in this

case, one method is not better than the other.

24

Topic 8

? Pearson Education, Inc. 6

Reteaching 8-2

3  21 using a whole number

Estimate __

10

that is compatible with the denominator.

3  21

__

Change 21 to the nearest

10

whole number that is

?

?

compatible with 10.

3  20  6

__

10

Name

Practice

Estimating Products

8-2

Sample answers are shown.

6 ? 5_

3 ?

2. 3 ? 2_15 ?

3. __

2

6

10

4

5. 6_12 ? 2_13 ?

6. _78 ? 2_38 ?

12

14

8. _14 ? 17 ?

9. _35 ? 51 ?

15

4

12 ? 8 ?

12. 11 ? _12 ?

42 11. __

4

25

5 ? 13 ?

15. __

6 14. 7__17 ? 2_23 ? 21

12

Estimate each product.

1. 4_58 ? _13 ?

4. 2_79 ? 4_25 ?

7. 38 ? _38 ?

10. 7_49 ? 5_67 ?

16. Show three ways to estimate _35 ? 5_34. Identify each method you use.

Sample answer: Compatible numbers: _35 ? 5 ? 3;

Rounding: 1 ? 6 ? 6; Compatible benchmark: _12 ? 6 ? 3.

3 miles from his office. He estimates that he

17. Explain It Mr. Simpson lives 11__

10

commutes 11 ? 2 ? 5, or 110 miles each week. Is his estimate an overestimate or an

underestimate? Explain.

Sample answer: 110 is an underestimate because

Mr. Simpson rounded the number of miles for each

trip to the lower whole number before he multiplied.

_

1

7

__

18. Which benchmark fraction could you use to estimate the product of 38 ?

12

?_______

2

19. Geometry Which is the best estimate for the area of a square with sides equal to 3_15

inches?

A

B

C

D

3 sq in.

6 sq in.

9 sq in.

16 sq in.

? Pearson Education, Inc. 6

9

20. Joyce and Marianne have money jars. Joyce has 54 dimes in her jar. Marianne has __

10

as many dimes as Joyce. Estimate the number of dimes that Marianne has in her jar.

A

B

C

D

60 dimes

45 dimes

6 dimes

5 dimes

Topic 8

25

Practice 8-2

4 ?

13. _89 ? 6__

10

3

2

30

6

5

Name

Reteaching

8-3

Multiplying Fractions

Find _34 ? _25.

Draw a picture.

Shade the squares.

There are 20 squares in all.

6 squares have overlapping shading.

3 ?_

6.

2 ? __

_

5

4

20

Use the

denominators to

determine the

number of

squares: 5 tall and

4 wide.

6 ? __

3

Simplify: __

20

10

Multiply the numerators and the

denominators. Simplify if possible.

(3 ? 2)

3 ?_

2 ? _____

_

5

4

(4 ? 5)

Reteaching 8-3

6

? __

20

Simplify first. Divide a numerator and a

denominator by their GCF. Then multiply.

3

_

4

(2 ? 2)

3

? _25 ? _____

? _____

5

(4 ? 2)

? _32 ? _15

3

? __

10

3

? __

10

Draw a picture to solve.

1. _13 ? _45 =

__

4

15

2. _34 ? _39 =

_

1

3. _12 ? _78 =

4

__

7

16

Write an equation for each picture.

5.

4.

_

3 ?_

2 ?_

1

4

3

2

Find each product. Simplify if possible.

3 =

6. _57 ? __

10

9. _56 ? _38 =

__

3

14

__

5

16

6 =

7. _12 ? __

15

5 =

10. _67 ? __

12

_

1

5

__

5

14

8. _47 ? _12 =

11. 8 ? _34 =

12. Number Sense Can you simplify before multiplying 14 ? _47 ? Explain.

30

_

2

7

6

Yes. Rewrite 14 as a fraction with 1 in the denominator.

Then simplify the 14 and the 7 using their

8 ? 8.

14 ? _

4?_

2?_

4?_

GCF of 7: __

7

1

1

1

1

Topic 8

? Pearson Education, Inc. 6

_

1 ?_

1 ?_

1

3

2

6

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download