DTR-Fractions and Decimals 3-4

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Fractions and Decimals34

Table of ContentsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

F R A C T I O N S

Identifying Parts of a Whole . . . . . . . . . . . . . . . . . . 4

Identifying Parts of a Group . . . . . . . . . . . . . . . . . . 5

Comparing FractionsLike Denominators . . . . 6

Comparing FractionsLike Numerators . . . . . . 7

Ordering Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Finding Equivalent Fractions . . . . . . . . . . . . . . . . 10

Simplest Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Fractional Part of a Number . . . . . . . . . . . . . . . . . 12

Parts of a Number . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Improper Fractions and Mixed Numbers . . . . . 14

Changing Improper Fractions to

Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Changing Mixed Numbers to

Improper Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Adding and Subtracting Fractions with

Like Denominators . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Adding Fractions with Unlike Denominators . . 18

Subtracting Fractions with Unlike

Denominators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Adding and Subtracting Fractions . . . . . . . . . . . 20

Adding Mixed Numbers . . . . . . . . . . . . . . . . . . . . . 21

Subtracting Mixed Numbers . . . . . . . . . . . . . . . . . 22

Problem Solving with Fractions . . . . . . . . . . . . . . 23

Fraction Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

More Fraction Review . . . . . . . . . . . . . . . . . . . . . . . 25

D E C I M A L S

Identifying Tenths . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Identifying Hundredths . . . . . . . . . . . . . . . . . . . . . 27

Decimals Greater Than 1 . . . . . . . . . . . . . . . . . . . . 28

Matching Fractions and Decimals . . . . . . . . . . . . 29

Comparing Tenths . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Ordering Tenths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Comparing and Ordering Hundredths . . . . . . . 32

Comparing and Ordering Fractions

and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Rounding Decimals . . . . . . . . . . . . . . . . . . . . . . . . . 34

Adding Tenths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Subtracting Tenths . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Adding and Subtracting Tenths . . . . . . . . . . . . . . 37

Adding Hundredths . . . . . . . . . . . . . . . . . . . . . . . . . 38

Subtracting Hundredths . . . . . . . . . . . . . . . . . . . . . 39

Problem Solving with Decimals . . . . . . . . . . . . . . 40

Decimals, Fractions, and Money . . . . . . . . . . . . . 41

Decimal Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Fraction and Decimal Equivalents . . . . . . . . . . . 43

Decimal Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

More Decimal Review . . . . . . . . . . . . . . . . . . . . . . . 45

Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3

Introduction

Fractions and Decimals 34 contains

ready-to-use activity pages to provide

students with skill practice. The fun

activities can be used to supplement

and enhance what you are already teaching

in your classroom. Give an activity page to

students as independent class work, or send

the pages home as homework to reinforce

skills taught in class. An answer key is included

at the end of the book.

This book provides activities that will directly

assist students in practicing basic skills and

concepts. The structure of the book enhances

students learning and enables them to meet

new challenges with confidence. The book

is divided into two sections: the first section

features fractions while the second presents

decimals. The pages in the book introduce

skills in an orderly progression to ensure

students success. Many of the pages also

provide problem-solving activities that allow

students to apply what they learned and to

practice critical thinking skills. In addition, two

review pages at the end of each section let

you evaluate students learning.

Students will receive reinforcement in the

following skills:

0 comparing fractions0 ordering fractions0 adding and subtracting fractions0 changing improper fractions to

mixed numbers

0 adding mixed numbers0 matching fractions and decimals0 comparing decimals0 ordering decimals0 rounding decimals0 adding and subtracting decimals

Use Fractions and Decimals Grades 34 to

reinforce or extend concepts and skills.

Recharge skill review with the ready-to-go

activities in this book, and give students the

power to succeed!

3

4 2

5.40

.75

4 Fractions

Name ____________________________________________________ Date __________________

Identifying Parts of a Whole

For each picture, write a fraction that tells what part is shaded and what part is not shaded.

A

C

E

G

B

D

F

H

The numerator tells how many parts you are comparing to the whole.

The denominator tells the total number of equal parts of a whole.

ShadedNot

Shaded ShadedNot

Shaded

ShadedNot

Shaded ShadedNot

Shaded

ShadedNot

Shaded ShadedNot

Shaded

ShadedNot

Shaded ShadedNot

Shaded

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4

Name ____________________________________________________ Date __________________

Identifying Parts of a Group

Write a fraction that tells what part is shaded.

A

The numerator tells what part you are comparing to a whole group.

The denominator tells the total number of parts in a whole group.

Fractions 5

B C

D E F

G H I

J Draw 5 fish. Color 15 of the fish red. Color 35 of them yellow.

What fraction of the fish are red or yellow? ___________

What fraction of the fish are not colored? ___________

Fractio

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2

5

2

3

3

4

1

3

2

4

2

5

5

8

4

5

7

8

4

6

5

6

3

5

1

5

6

8

1

8

2

9

3

9

5

7

6

7

2

10

9

10

4

12

7

12

4

8

3

8

6 Fractions

Name ____________________________________________________ Date __________________

Comparing FractionsLike DenominatorsColor the bars to make them match the fractions in each pair. Circle the greater fraction.

A

Compare the fractions. Write > or < in the circles.

B

C D

E

F

G Jim and Kate each had a strip of paper 24 inches long. Jim used 38 of his strip. Kate used 58 of her strip. Who used more paper? _______

Brett and Kylie each had a piece of ribbon 18 inches long. Brett used 26 of his ribbon for an art project. Kylie used 36 of her ribbon. Who had more ribbon left? __________________

If two fractions have the same denominator, how can you tell which one is

greater?__________________________________________________

H

I

36 and 56

have the same

denominator.

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A pepperoni pizza and a mushroom pizza were the same size.Kris ate 210 of the pepperoni pizza.Lee ate 28 of the mushroom pizza.

Who ate more pizza? _______________________

Evan and Lori were making pizzas.Evan sprinkled 23 cup of grated cheese on his pizza.Lori sprinkled 24 cup of cheese on her pizza.

Who used more cheese? _______________________

Mr. Burtons class did a survey to see which pizza topping was the most popular.One fourth of the students chose cheese.One half of the students chose pepperoni.One sixth of the students chose ham.

Which topping was the most popular? _______________________

Of the three toppings, which one was the least popular? ____________________

Fractions 7

Name ____________________________________________________ Date __________________

Comparing FractionsLike NumeratorsWhen comparing fractions that have the same numerator, look at the denominators. The fraction with the smaller denominator is larger.

D

E

F

>

1

5

1

2

2

7

2

6

3

4

3

5

7

8

7

10

2

3

2

6

5

8

5

10

4

9

4

5

9

12

9

10

7

12

7

11

6

9

6

8

2

4

2

6

8

10

8

12


A

B

C

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1

2

1

3

and 13

have the same

numerator.

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8 Fractions

Name ____________________________________________________ Date __________________

Ordering Fractions Write the fractions in order from the least to the greatest.

A B

______________________________________ ______________________________________

C D

______________________________________ ______________________________________

E F

______________________________________ ______________________________________

G H

______________________________________ ______________________________________

I J

______________________________________ ______________________________________

4

5

1

5

3

5

2

5

3

6

5

6

4

6

2

6

7

10

2

10

5

10

9

10

6

8

3

8

1

8

5

8

1

9

1

6

1

5

1

8

2

7

2

4

2

10

2

3

5

12

5

8

5

7

5

11 3

4

3

12

3

10

3

8

4

5

4

8

4

6

4

9

6

8

6

10

6

12

6

7

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Name ____________________________________________________ Date __________________

Equivalent Fractions

Use the pictures below to help you write equivalent fractions.

A

Fractions 9

B C

D E F

G

Fractions that describe the same amount are called equivalent fractions.

Use the fraction bars to help you write equivalent fractions.

H

I

1

2 6=

1

3 6=

1

4 8=

3

5 10=

1

2 8=

2

3 6=

2

4 8=

3

4 8=

1

3 9=

2

3 9=

2

2 4=

3

3 6=

and 24

are equivalent

fractions.1

2

2

4

1 whole

18

18 18 18 18 18 18 18

1 whole

13

16

13 13

16 16 16 16 16

19 19 19 19 19 19 19 19 19

10 Fractions

Name ____________________________________________________ Date __________________

Finding Equivalent Fractions

Multiply to find equivalent fractions.

2

4

1

2=

2

2

1

2

3

6=

3

3

=1

3 6

2

2A =

1

2 8

4

4=

1

4 12

3

3

Divide to find equivalent fractions.

=4

10 5

2

2B =

4

8 2

4

4=

3

9 3

3

3

Write equivalent fractions.

C

D

E

1

2 =

10

1

2 =

12

1

3 =

12

6

8 =

4

3

12 =

4

2

8 =

4

9

12 =

4

2

3 =

15

6

10 =

5

Equivalent fractions

show the same amount.

You can divide to

find equivalent fractions.

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You can multiply to find

equivalent fractions.

1

4

2

4

3

4 ________

11

12

7

12

9

12 ________

7

8

5

8

2

8 ________

5

10

3

10

7

10 ________

3

6

1

6

5

6 ________

8

9

6

9

4

9

________

Name ____________________________________________________ Date __________________

Simplest Form

Fractions 11

A fraction is in simplest form when 1 is the only number that can divide both the numerator and the denominator evenly.

Write each fraction in simplest form.

46 is not in simplest form because 4 and 6 are both divisible by 2.

23 is in simplest form because the only number that divides 2 and 3 evenly is 1.

Look at each row. Circle the fraction that is not in simplest form. Then write it in simplest form.

A B

C D

E F

G

I

H

2

3

4

6=

2

2

2

6 =

3

9 =

8

10 =

3

12 =

4

8 =

10

12 =

3

15 =

6

8 =

4

12 =

6

10 =

6

12 =

10

15 =

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2

3

2

3=

1

1

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12 Fractions

Name ____________________________________________________ Date __________________

Fractional Part of a Number

Circle to make 2 equal groups. Then color the balloons in 1 group to help you solve each problem.

A

You can use pictures of equal groups to find the fraction of a number.


B


C

1

2 of 4 = ________

1

2 of 8 = ________

1

2 of 6 = ________

1

3 of 3 = ________

1

3 of 9 = ________

1

3 of 12 = ________

1

4 of 8 = ________

1

4 of 4 = ________

1

4 of 12 = ________

1

3 of 6 = 2

Fractions 13

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2

3 of 15 = _____

4

6 of 12 = _____

1

8 of 16 = _____

3

4 of 8 = _____

2

7 of 21 = _____

2

5 of 20 = _____

8

9 of 18 = _____

5

8 of 16 = _____

3

9 of 18 = _____

5

7 of 14 = _____

3

5 of 15 = _____

2

3 of 12 = _____

7

10 of 20 = _____

5

6 of 18 = _____

4

5 of 15 = _____

Name ____________________________________________________ Date __________________

Parts of a NumberThere are 20 beads. Three fourths of them are blue.What is of 20?

You can use division and multiplication to help you find the answer.

Solve.

A

D

B

E

C

1. First, divide 20 by 4 to find out how many beads there are in 4 equal groups.

There are 5 beads in each group.

2. Next, multiply that number by 3 to find out how many beads there are in 3 groups.

There are 15 beads in 3 groups. That means of 20 equals 15.

20 4 = 5 3 5 = 15

Name ____________________________________________________ Date __________________

Improper Fractions and Mixed Numbers

Write an improper fraction and a mixed number to describe the shaded parts in each picture.

A B C

D E F

G H I

Matt cut some paper circles into halves. You can describe his shapes by using an improper fraction or a mixed number.

An improper fraction has a numerator that is greater than or equal to the denominator. A mixed number has a whole number and a fraction.

Some improper fractions equal a whole number. Write an improper fraction and a whole number to describe the shaded parts in each picture below.

14 Fractions

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7

2

1

23 =

2

21 =

4

22 =

Name ____________________________________________________ Date __________________

Changing Improper Fractions to Mixed Numbers

Megan has 5 sandwich halves. She groups the halves together to make whole sandwiches. How many whole sandwiches can she make? The picture shows that Megan will make 2 whole sandwiches and have 1 half left over.

D

3

2 = _______

6

3 = _______

7

5 = _______

9

4 = _______

9

3 = _______

11

2 = _______

15

4 = _______

8

7 = _______

8

4 = _______

12

5 = _______

11

8 = _______

15

3 = _______

To change an improper fraction to a mixed number, divide the numerator by the denominator to get the number of wholes and the number of fractional parts.

A

B

C

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Kelly made sandwiches for her party. She cut the sandwiches into halves and placed them on a large plate. Kelly counted 16 sandwich halves. How many whole sandwiches did she make?

_________ sandwiches

Mike cut sandwiches into fourths. When he was done, he counted 24 fourths in all. How many whole sandwiches did Mike cut?

_________ sandwiches

E

Change the improper fractions to mixed numbers or whole numbers.

5

22

1

2=

)52

2 52

-4

1

number of wholes

number of halves left over

Fractions 15

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Changing Mixed Numbers to Improper Fractions

Bettys Bakery has only 2 pies left. How many fourths is that? To find out, first figure out how many fourths there are in 2 wholes. Do this by multiplying 2 4. That gives you 8 fourths. Then add that number to the remaining fourth to get 9 fourths in all.

D

11

2= _______

13

4= _______

15

8= _______

11

3= _______

21

2= _______

31

4= _______

54

5= _______

23

8= _______

32

3= _______

61

10= _______

41

3= _______

34

5= _______

To change a mixed number to an improper fraction, first multiply the whole number by the denominator. This tells you the number of parts there are in the whole number. Then add that number to the number of leftover parts. This will give you the total number of parts.

A

B

C

Glen brought 10 bagels to school. The teacher cut them into thirds. There are 21 students in Glens class. Are there enough pieces for each student to get 13 bagel? Explain. _____________________________

_____________________________

Marias cake recipe uses 3 cups of flour. She only has a -cup measur-ing cup. How many times will Maria need to fill the cup?

_________ times

E

Change the mixed numbers to improper fractions.

4

4

4

4

1

4

21

4(2 4) + 1 = 9

number of

fourths in 2

number of

leftover

fourths

total number

of fourths

16 Fractions

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21

4

9

4 =

Fractions 17

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Adding and Subtracting Fractions with Like Denominators

Color the parts to show addition. Then write the answers.

A

Cross out the parts to show subtraction. Then write the answers.

C

Add or subtract.

E

B

D

F

1

4

2

4+ =

3

4

1

3

1

3+ =

2

5

2

5+ =

2

7

3

7+ =

6

9

4

9 = 3

10

4

10+ =

4

6

2

6 =

2

9

5

9+ =

7

10

6

10 = 1

7

5

7+ =

6

10

3

10+ =

1

6

4

6+ =

1

5

2

5+ =

3

8

2

8+ =

4

5

2

5 = 2

5

2

3

1

3 = 3

4

1

4 =

7

8

4

8 = 5

6

4

6 = 9

10

7

10 =

1

3

3

6+ =

2

5

5

10+ =

5

8

1

4+ =

1

2

1

5+ =

2

3

1

4+ =

Name ____________________________________________________ Date __________________

Adding Fractions with Unlike Denominators

When adding two fractions that have different denominators, first change the fractions to equivalent fractions that have the same denominator. Then add.

Add.

A

G

C

I

E

1

2

1

4

1

4

3

4+ = + =

2

4

1

2

1

3

5

6+ = + =

3

6

2

6

2

6

1

12+ =

3

8

1

2+ =

2

3

2

9+ =

1

3

1

4+ =

3

4

3

16+ =

B

H

D

J

F

K Mr. Morgan is driving his truck to Boomsville. By 11:00, he has driven of the distance. He drives another 18 of the way by noon. What frac-tion of the trip has he completed by noon? ________ of the trip

There are several trucks rolling along the highway. Two fifths of the trucks are red and of them are black. What fraction of the trucks are either red or black?________ of the trucks

L

18 Fractions

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Sometimes you only have

to rename one fraction.Sometimes you have to

rename both fractions.

Fractions 19

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2

3

1

9 =

4

6

1

2 =

7

8

1

2 =

1

3

1

4 =

3

5

1

4 =

Name ____________________________________________________ Date __________________

Subtracting Fractions with Unlike Denominators

When subtracting fractions that have different denominators, first change the fractions to equivalent fractions that have the same denominator. Then subtract.

Subtract.

A

G

C

I

E

3

4

1

8

1

8

5

8 = =6

8

1

2

1

3

1

6 = =3

6

2

6

7

12

1

6 =

2

5

1

4 =

2

3

3

7 =

5

8

1

2 =

2

3

5

9 =

B

H

D

J

F

K Bert ran 23 of a mile on Friday. He ran of a mile on Saturday. How much farther did he run on Friday than on Saturday?

________ mile

Marcy had 79 yard of ribbon. She used 13 yard for an art project. How much ribbon did she have left?

________ yard

L

Sometimes you only have to

rename one fraction.Sometimes you have to

rename both fractions.

1

6

2

6+ =

3

8

1

8 =

4

12

6

12+ =

7

9

4

9 =

9

10

3

10 =

Name ____________________________________________________ Date __________________

Adding and Subtracting FractionsAdd or subtract. Write the answers in simplest form.

Add or subtract. Write answers in simplest form.

A

G

C

I

E

58

18

68

6 28 2

34

+ = = =

1112

312

812

8 412 4

23

= = =

7

15

5

15+ =

11

12

8

12 =

3

4

1

4 =

1

12

1

12+ =

15

16

5

16 =

B

H

D

J

F

1

4

1

12+ =

8

10

3

5 =

2

3

3

9+ =

Add or subtract. (Remember to rename the fractions in each problem so that they have the same denominator.) Write the answers in simplest form.

K

M

O

1

6

7

12+ =

5

9

1

18 =

7

9

1

18+ =

L

N

P

20 Fractions

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4

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21

5

22

5+

51

6

43

6+

33

8

24

8+

61

2

41

2+

12

3

42

3+

83

7

21

7+

63

10

52

10+

93

8

26

8+

81

9

62

9+

45

12

33

12+

18

9

66

9+

73

10

89

10+

Name ____________________________________________________ Date __________________

Adding Mixed NumbersWhen adding mixed numbers, add the fractions first. Change any improper fractions to mixed numbers. Then add the whole numbers. Write the answer in simplest form.

A

B

C

Add 16 and 16.

Add 3 and 2.

52

65

2 2

6 25

1

3

= =

Add 35 and 45.

Add 2 and 5.

7 7 1 82

5

7

5

2

5 = + =

Fractions 21

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31

6

21

6+

23

5

54

5+

48

9

24

9

61

2

51

2

35

6

33

6

79

10

42

10

53

4

21

4

34

5

32

5

75

8

63

8

611

12

310

12

89

10

35

10

47

9

14

9

67

12

25

12

99

10

34

10

Name ____________________________________________________ Date __________________

Subtracting Mixed NumbersWhen subtracting mixed numbers, subtract the fractions first. Then subtract the whole numbers. Write the answers in simplest form.

A

B

C

Subtract 38 from 78.

Subtract 1 from 4.

22 Fractions

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47

8

13

8

34

83

4 4

8 43

1

2

= =

Fractions 23

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Name ____________________________________________________ Date __________________

Problem Solving with FractionsSolve.

A

C

E

G

B

D

F

H

Brian cut out 15 paper shapes. Two thirds of the shapes were circles. The rest were triangles. How many shapes were triangles?

____________ triangles

Amy had 16 markers in a box. She put 58 of the markers on her desk. How many markers were on her desk?

There were 18 students working with clay. Two thirds of the class made pots. How many students made pots?

Cindy had yarn that was 20 inches long. She cut the yarn in half. Then she cut each piece in half again. How long was each piece?

Mr. Jackson had 30 paintbrushes in a can. After he passed out the brushes to the class, only 15 of the brushes were left in the can. How many students are in Mr. Jacksons class?

____________ students

Mrs. Lane put her students pictures on the wall. She arranged them in 6 rows with 4 pictures in each row. She saw that 13 of the pictures were of pets. How many pictures showed pets?

____________ pictures

Justin had a box of 12 crayons. He took one half of the crayons out of the box. Then he put 3 crayons back in the box. What fraction of the crayons were out of the box?

_______ of the crayons

Miss Wus class made 36 paper flowers. One half of the flowers were red. One third of the flowers were yellow. The rest were blue. What fraction of the flowers were blue?

________ of the flowers

____________ students ____________ inches

____________ markers

12 6=

1

4 8=

1

3 6=

1

2 8=

2

3 6=

2

4 2=

6

8 4=

8

10 5=

Name ____________________________________________________ Date __________________

Fraction ReviewWrite the fraction that tells what part is shaded.

A

Write equivalent fractions.

B

D

E

4

7

3

7

2

6

2

3

5

10

5

8

9

12

4

12


C

3

9=

5

10=

2

8=

9

12=

Write each fraction in simplest form.

F

Use the pictures to answer the questions.

What is of 8? ________

What is of 8? ________

H

J

What is of 6? _______

What is 13 of 6? ________

G

I

24 Fractions

Fra

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4

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Pre

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Write an improper fraction and a mixed number to describe the shaded parts.

_________________L _________________K

Name ____________________________________________________ Date __________________

More Fraction ReviewAdd. Write the answers in simplest form.

A 1

4

1

4+ =

3

6

1

6+ =

2

9

4

9+ =

2

3

2

3+ =

5

8

3

8+ =

9

10

9

10+ =

1

3

1

6+ =

1

2

1

4+ =

3

8

1

4+ =

21

5

43

5+

31

10

51

10+

53

8

16

8+

42

3

61

3+

B

C

D

Subtract. Write the answers in simplest form.

E 5

8

2

8 =

7

10

3

10 =

8

9

2

9 =

1

3

1

4 =

5

8

1

2 =

11

12

2

12 =F

G A pizza was divided into 8 equal pieces. Sarah ate of the pizza. Kyle ate twice as much as Sarah. What fraction of the pizza was left?

__________ of the pizza

Explain how you got the answer to problem G.

_____________________________

_____________________________

H

Solve. Write your answer in simplest form.

Fractions 25

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Name ____________________________________________________ Date __________________

Identifying Tenths

Fill in the chart.

A

26 Decimals

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= 0.7 = seven tenths7

10

Word Form

B

C

D

E

F

G

Fraction Decimal

3

100.3

AF

three tenths

________ tenths

________ tenths

________ tenths

________ tenths

________ tenths

________ tenths

Name ____________________________________________________ Date __________________

Identifying Hundredths

Write a fraction and a decimal to describe the shaded part of each picture.

32

1000 32 .=

A

B

C

Color the squares to match each decimal.

____________ ____________ ____________

____________ ____________ ____________

0.55 0.80 0.06D E

Decimals 27

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60

1000 60 .=

9

1000 09 .=

Name ____________________________________________________ Date __________________

Decimals Greater Than 1

Write a mixed number and a decimal to describe the shaded parts.

15

101 5 .=

A

B

C

Write each mixed number as a decimal.

____________ ____________ ____________

____________ ____________ ____________

316

100 ______ 7

5

10 ______ 9

89

100 ______ 4

1

10 ______

249

1002 49 .=

28 Decimals

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0.3 ________ 0.4 ________ 0.9 ________ 0.17 ________

0.01 ________ 0.83 ________ 0.03 ________ 0.1 ________

Name ____________________________________________________ Date __________________

Matching Fractions and Decimals

Write the matching fractions.

A

B

210 _______

7

10 _______

95

100 _______

61

100 _______

85

100 _______

2

100 _______

46

100 _______

5

100 _______

Write the matching decimals.

C

D

7.7 _________ 12.03 _______ 5.3 ________ 11.4 ________

8.09 ________ 4.59 ________ 6.02 ________ 15.01 ________

Write the matching mixed numbers.

E

F


Decimals 29

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31

10 _______

57

10 _______

1035

100 _______

465

100 _______

99

100 _______ 14

310

_______

171

10 _______

71

100 _______

G

H

Name ____________________________________________________ Date __________________

Comparing TenthsColor the pictures to match the decimals. Then circle the greater decimal in each pair.

A B0.7

0.5

0.6

0.9

C D1.6

1.2

1.8

1.9

0.2 0.4

Compare the decimals. Write > or < in the circles.

E 0.5 0.1 0.9 0.7 0.3 0.4

1.5 1.6F 1.4 1.6 2.3 1.3 2.5 5.2

G Pat ran 1.2 miles. Kelly ran 1.3 miles. Who ran farther?

____________________

Janet lives 2 blocks from school. Randy lives 1.9 blocks from school. Who lives farther from school? ______________________

H

Solve.

30 Decimals

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4

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__________ __________ __________ __________

__________ __________ __________ __________

Name ____________________________________________________ Date __________________

Ordering TenthsWhich decimals are missing from the number line? Write them beside the matching letters. Use the decimals in the box.

A

E

Look at the decimals in each set. Write them in order from least to greatest.

0.5 1.2 0.3 0.8

0.9 1.6 0.2 1.3

B

F

C

G

D

H

0.9 _________

0.2 _________

0.3 _________

0.7 _________

1.3 _________

1.6 _________

1.8 _________

1.5 _________

2.0 _________

1.3 _________

0.6 _________

0.9 _________

I J K

Write the next four decimals.

0.1, 0.2, 0.3, 0.4, _______, _______, _______, _______

5.1, 5.2, 5.3, 5.4, _______, _______, _______, _______

7.5, 7.6, 7.7, 7.8, _______, _______, _______, _______

4.9, 4.8, 4.7, 4.6, _______, _______, _______, _______

8.6, 8.5, 8.4, 8.3, _______, _______, _______, _______

12.4, 12.3, 12.2, 12.1, _______, _______, _______, _______

L

M

N

O

P

Q

Decimals 31

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0 0.1

A B

0.4

C

0.6 0.7

D E

1.0 1.1

F G

1.4 1.5

H

Name ____________________________________________________ Date __________________

Comparing and Ordering HundredthsColor the pictures to match the decimals. Then compare the decimals in each pair. Write >, ,

__________ __________ __________ __________

__________ __________ __________ __________

Name ____________________________________________________ Date __________________

Comparing and Ordering Fractions and Decimals

Circle the greatest number. Draw a box around the smallest number.

H

L

Write the numbers in order from least to greatest.

1.4 1.82 0.35 0.75

1.25 0.9 0.2 1.7

I

M

J

N

K

O

0.7 _________

0.09 _________

0.9 _________

0.79 _________

1.2 _________

1.08 _________

1.5 _________

1.28 _________

_________

0.39 _________

_________

0.3 _________

E F G

Find the decimals that are missing from the number line. Write them

beside the matching letters. Use the numbers in the box.

A B0.23 0.32 30

100

4.6 4.46 440

100

2.1 2.15 25

10

9.78 9.8 97

10

4

10

16

100

Decimals 33

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C D

0

H I

510

J K

1

L M

1510

N O

2

7.6 ________ 3.5 ________ 9.2 ________ 8.1 ________

3.4 ________ 9.6 ________ 12.8 ________ 11.4 ________

5.91 ________ 16.34 ________ 14.52 ________ 2.78 ________

Name ____________________________________________________ Date __________________

Rounding DecimalsWhen rounding decimals to the nearest whole number, look at the number in the tenths place. If it is 5 or greater, round up to the next whole number. If it is less than 5, keep the whole number as is.

A

B

When rounding decimals to the nearest tenth, look at the number in the hundredths place. If it is 5 or greater, round up to the next tenth. If it is less than 5, keep the tenth as is.

Round to the nearest whole number.

C

1.38 ________ 6.07 ________ 5.82 ________ 9.49 ________

20.87 ________ 15.38 ________ 26.55 ________ 11.13 ________

0.63 ________ 17.03 ________ 40.09 ________ 32.75 ________

D

E

Round to the nearest tenth.

F

G A bull stands 5.3 feet tall. What is its height rounded to the nearest foot?

_______ feet

A rope is 6.27 meters long. What is its length rounded to the nearest tenth of a meter?

_______ meters

H

Solve.

34 Decimals

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4

20

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3.7 The number in the tenths place is 7.

Round 3.7 to 4.

3.2 The number in the tenths place is 2.

Round 3.2 to 3.

2.48 The number in the hundredths place

is 8. Round 2.48 to 2.5.

2.43 The number in the hundredths place

is 3. Round 2.43 to 2.4.

0 20 4

. .+

0 80 9

. .+

0 43 4

. .+

1 21 7

.

.+

5 69 4

. .+

8 30 9

. .+

12 416 7

. .+

25 325 7

. .+

17 819 0

. .+

32 56 7

. .+

23 66 8

. .+

14 519 3

. .+

37 930 7

. .+

4 421 0

. .+

20 719 3

. .+

Name ____________________________________________________ Date __________________

Adding TenthsAdding tenths is similar to adding whole numbers. Add the columns one at a time, beginning with the far right. Regroup if needed. Remember to bring down the decimal and include it in the answer.

A

B

Add.

C

D

Complete each chart.

0 52 3

. .+

1. Add the tenths.2. Add the ones.

0 52 3

. .+

2.8

4 63 7

. .+

1. Add the tenths.There are 13 tenths.Write down the 3 and place the 1 above the ones column.

4 63 7

. .+

.3

1

2. Add the ones.

4 63 7

. .+

8.3

Input Output

5.0

0.6

1.9

E

Input Output

0.4

1.5

F

3.2

Add 0.3 Add 1.5 Add 4.7

Input Output

2.1

3.2

5.9

Decimals 35

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1

7 52 4

. .

3 60 4

. .

11 89 4

. .

6 52 8

. .

24 17 6

. .

20 53 8

. .

18 69 2

. .

32 42 5

. .

45 928 7

. .

68 818 9

. .

38 716 4

. .

24 59 8

. .

37 619 5

. .

73 670 8

. .

52 417 6

. .

Name ____________________________________________________ Date __________________

Subtracting TenthsSubtracting tenths is similar to subtracting whole numbers. Subtract the columns one at a time beginning at the far right. Regroup if needed. Remember to bring down the decimal and include it in the answer.

A

B

Subtract.

C

5 91 2

. .

1. Subtract the tenths.

2. Subtract the ones.

5 91 2

. .4.7

8 53 6

. .

1. Regroup the ones to

make 7 ones and 10 tenths.

Combine the 10 tenths

with the 5 tenths to get 15

tenths.

8 53 6

. .7 15

2. Subtract the tenths.

Then subtract the ones.

4.9

8 53 6

. .7 15

D Mr. Cooper had a box of nails that weighed 18.5 ounces. After he used some nails, the box weighed 12.8 ounces. What was the weight of the nails that he used?

___________ ounces

Beckys board is 60.3 centimeters. Matts board is 49.5 centimeters. How much longer is Beckys board

than Matts?

___________ centimeters

E

Solve.

36 Decimals

Fra

ctio

ns

an

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3

4

20

07

Cre

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4 32 5

. .+

0 96 9

. .+

7 60 3

. .+

15 23 8

. .+

28 17 6

. .+

12 31 3

. .

18 43 6

. .

20 99 4

. .

31 412 5

. .

25 46 3

. .

36 00 8

. .+

25 716 4

. .+

59 313 8

. .

28 46 8

. .

15 215 8

. .+

54 648 3

. .

62 917 8

. .

43 29 9

. .+

7 320 8

. .+

66 323 6

. .

2 63 54 2

.

. .+

1 213 4

9 5

.

. .+

0 60 57 4

.

. .+

9 318 214 5

.

. .+

3 86 4

12 3

.

. .+

Name ____________________________________________________ Date __________________

Adding and Subtracting TenthsAdd or subtract.

A

B

C

F Choose an addition problem you solved. Write a word problem that matches it.

______________________________

______________________________

______________________________

Choose a subtraction problem you solved. Write a word problem that matches it.

______________________________

______________________________

______________________________

G

Solve.

D

E

Decimals 37

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7 211 63

. .+

8 341 92

. .+

5 50 67

. .+

2 91 84

. .+

0 930 6

. .+

4 817 99

. .+

2 670 14

. .+

4 83 44

. .+

3 95 72

. .+

5 611 32

. .+

19 818 37

. .+

23 655 6

. .+

17 083 5

. .+

2 4618 08

. .+

32 79 03

. .+

Name ____________________________________________________ Date __________________

Adding HundredthsAdding hundredths is similar to adding tenths. When adding tenths to hundredths, change the tenths to hundredths by adding a 0 in the hundredths place. Then add. Regroup if needed.

A

B

Add.

C

4 352 13

. .+

1. Add the hundredths.2. Add the tenths.3. Add the ones.

4 352 13

. .+

6.48

6 53 25

. .+

1. Add 0 to the end of 6.5 so that it has two decimal places like 3.25.

6 53 25

. .

0

+

2. Add the columns one at a time, beginning with the hundredths.

9.75

6 503 25

. .+

D A can of oranges weighed 11.5 ounces. A can of pears weighed 15.75 ounces. How much did the cans weigh altogether?

___________ ounces

One package of onion soup mix weighed 28.35 grams. What did two packages of the mix weigh?

___________ grams

E

Solve.

38 Decimals

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4

20

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.5 754 23

.

9 865 34

. .

2 340 13

. .

14 856 49

. .

26 859 8

. .

37 416 24

. .

45 3219 1

. .

57 8634 3

. .

23 920 8

. .

15 736 99

. .

65 273 1

. .

18 073 5

. .

39 116 55

. .

40 8329 2

. .

63 528 46

. .

50 079 5

. .

Name ____________________________________________________ Date __________________

Subtracting HundredthsSubtracting hundredths is similar to subtracting tenths. When subtracting tenths from hundredths, change the tenths to hundredths by adding a 0 in the hundredths place. Then subtract. Regroup if needed.

A

B

Subtract.

C

5 754 23

. .

1. Subtract the hundredths.2. Subtract the tenths.3. Subtract the ones.

1.52

6 43 29

. .

1. Add 0 to the end of 6.4 so that it has two decimal places like 3.29.

6 43 29

. .

0

2. Subtract the columns one at a time, beginning with the hundredths.

3.11

6 403 29

. .

D Brent lives 10.75 miles from the beach. Jessica lives 4.8 miles from the beach. How much farther does Brent live from the beach than Jessica?

___________ miles

Loris surfboard is 6.25 feet long. Kents surfboard is 7.4 feet long. How much longer is Kents board than Loris?

___________ feet

E

Solve.

Decimals 39

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3 10

Dog WeightsHow much do the two lightest dogs weigh altogether?

____________________

How much do the two heaviest dogs weigh altogether?

____________________

What is the difference in weight between the heaviest dog and the lightest dog?

____________________

Which two dogs have a total weight of 35.84 pounds? _____________________

Which dog weighs about 17 pounds less than Fangs? ______________________

Is Scooter more or less than 10 pounds? _______________________________

How do you know? __________________________________________________

___________________________________________________________________

Suppose Wags and Pepper got on a scale together. Would they weigh more or

less than Fangs?

____________________

How much would they weigh? __________________

Name ____________________________________________________ Date __________________

Problem Solving with DecimalsThe chart shows the weights of five dogs. Use the chart to answer the questions.

A

B

DogWeight in

Pounds

Ruff

Pepper

Wags

Scooter

Fangs

25.45

12.5

30.6

10.39

42.8

40 Decimals

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C

D

E

F

G

83 = __________ of a dollar

19 = __________ of a dollar

21 = __________ of a dollar

$0.49 = __________ of a dollar

$0.37 = __________ of a dollar

$0.99 = __________ of a dollar

Name ____________________________________________________ Date __________________

Decimals, Fractions, and MoneyOne hundred pennies is worth 100 cents, or 1 dollar. You can write the amount as 100 or $1.00. You can use fractions to show how the value of coins can be written as a decimal amount.

A

C

E

Write each amount as a fraction of a dollar.

B

D

F

G Julie has 70 pennies. She says she has 710 of a dollar. Is she right? Explain why or why not.

_____________________________________

_____________________________________

CoinNumber of Cents

penny

nickel

dime

quarter

half dollar

1

______

______

______

______

Fraction of a Dollar

Decimal Amount

1

100

$0.01

CoinNumber of Cents

8 pennies

5 nickels

7 dimes

3 quarters

2 half

dollars

______

______

______

______

______

Fraction of a Dollar

Decimal Amount

Decimals 41

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Fill in the chart.

0.2, 0.4, 0.6, 0.8, __________, __________, __________, __________

What number was added each time? _________

0.05, 0.10, 0.15, 0.20, __________, __________, __________, __________

What number was added each time? _________

1.3, 1.2, 1.1, 1.0, __________, __________, __________, __________

What number was subtracted each time? _________

1.0, 0.89, 0.78, 0.67, __________, __________, __________, __________

What number was subtracted each time? _________

Name ____________________________________________________ Date __________________

Decimal Patterns

Study the patterns. Then add the next four numbers to each pattern.

A

B

C

D

E

F

G

Lisa walked 0.5 miles on Monday. Each day after that, she walked 0.2 miles more than the day before. How many miles did she walk altogether after 4 days?

___________________

Jakes plant grows 0.15 centimeters a day. On Sunday, his plant is 10.15 centimeters tall. How tall will the plant be next Friday?

___________________

Carla arranged 5 bags of fruit on a shelf. Each bag was 0.25 pounds less than the bag to its left. The bag on the far left weighed 3.25 pounds. How much did the bag on the far right weigh?

___________________

Use patterns to solve the problems.

42 Decimals

Fra

ctio

ns

an

d D

eci

ma

ls

3

4

20

07

Cre

ati

ve

Te

ach

ing

Pre

ss

Name ____________________________________________________ Date __________________

Fraction and Decimal EquivalentsYou can easily change certain fractions into decimals.

Fractions that have a denominator of 10 or 100

Use the numerator to help you write the decimal.

7

10=

______

85

100=

______

1

5=

______

2

5=

______

2

10=

______

1

4=

______

17

100=

______

9

100=

______

3

20=

______

48

50=

______

3

4=

______

1

25=

______

93

100=

______

10

20=

______

12

25=

______

4

5=

______

33

50=

______

19

25=

______

11

20=

______

21

25=

______

Fractions that can be changed to tenths or hundredths

Find an equivalent fraction that has a denominator of 10 or 100. Then use the numerator of that fraction to help you write the decimal.

A

B

C

Change the fractions to decimals. If you need to, change them to tenths or hundredths first.

D

E

Decimals 43

Fractio

ns a

nd

De

cima

ls 3

4

20

07

Cre

ativ

e Te

ach

ing

Pre

ss

3

100 3 . 45

1000 45 .

1

2

1

2

5

5

5

100 5 = . 1

2

1

2

50

50

50

1000 50 = .

Name ____________________________________________________ Date __________________

Decimal ReviewWrite a fraction and a decimal to describe the shaded part of each picture.

Write the numbers in order from the least to the greatest.

0.68 _________

0.8 _________

0.86 _________

0.6 _________

0.49 _________

0.3 _________

0.05 _________

0.7 _________

1.2 _________

1.02 _________

1.12 _________

1.21 _________

D E F

3.5 ________ 5.7 ________ 2.19 ________ 9.58 ________G

Round to the nearest whole number.

A

____________ ____________ ____________

8.76 ________ 9.03 ________ 12.65 ________ 14.29 ________H

Round to the nearest tenth.

0.7 _________ 0.9 _________ 0.27 _________ 0.03 _________B

Write the matching fractions.


44 Decimals

Fra

ctio

ns

an

d D

eci

ma

ls

3

4

20

07

Cre

ati

ve

Te

ach

ing

Pre

ss

6

10 ______

25

100 ______

6

100 ______

9

1

10 ______

C

Decimals 45

Fractio

ns a

nd

De

cima

ls 3

4

20

07

Cre

ativ

e Te

ach

ing

Pre

ss

0 80 9

. .+

1 59 3

. .+

3 40 4

. .

7 61 8

. .

9 87 7

. .+

12 426 13

. .

9 068 04

. .

15 618 33

. .

20 056 24

. .

13 429 65

. .

7 58 43

. .+

4 76 52

. .+

18 69 43

. .

24 512 86

. .

30 79 83

. .+

52 6218 9

. .+

14 0325 7

. .+

26 3416 8

. .

39 069 4

. .

17 3518 5

. .+

6 32 854 03

.

. .+

12 97 5

15 06

.

. .+

16 374 283 9

.

. .+

5 37 648 4

.

. .+

14 8712 09

6 3

.

. .+

Name ____________________________________________________ Date __________________

More Decimal ReviewAdd or subtract.

A

B

C

F Choose an addition problem from above. Write a subtraction problem that has the same answer.

_____________________________

______________________________

Choose a subtraction problem from above. Write an addition problem that has the same answer.

______________________________

______________________________

G

Solve.

D

E

Identifying Parts of a Whole (page 4)

A. ,

B. 25, 35

C. 23, 13

D. 38, 58

E. 56, 16

F. 710, 310

G. 58, 38

H. 810, 210

Identifying Parts of a Group (page 5)

A. 13

B. 45

C.

D. 59

E. 27

F. 56

G. 38

H. 23

I. 710

J. 45, 15

Comparing FractionsLikeDenominators (page 6)

AD: Bars should be colored accordingly.

A. 23

B.

C. 45

D. 78

E. < > >

G. Kate

H. Brett

I. The fraction with the larger numerator

is greater.

Comparing FractionsLike Numerators(page 7)

A. < < > >

B. > > < >

D. Lee

E. Evan

F. most popularpepperoni

least popularham

Ordering Fractions (page 8)

A. 15, 25, 35, 45

B. 26, 36, 46, 56

C. 210, 510, 710, 910

D. 18, 38, 58, 68

E. 19, 18, 16, 15

F. 210, 27, 24, 23

G. 512, 511, 58, 57

H. 312, 310, 38,

I. 49, 48, 46, 45

J. 612, 610, 68, 67

Equivalent Fractions (page 9)

A. 36

B. 26

C. 28

D. 610

E. 48

F. 46

G. 48, 68

H. 39, 69

I. 44, 66

Finding Equivalent Fractions (page 10)

A. 26, 48, 312

B. 25, , 13

C. 510, 612, 412

D. , ,

E. , 1015, 35

Simplest Form (page 11)

A. 24

B. 912

C. 28

D. 510

E. 36

F. 69 23

G. 13, 13, 45,

H. , 56, 15,

I. 13, 35, , 23

Fractional Part of a Number (page 12)

Balloons should be circled to form 2 equal

groups.

A. 2 balloons colored; 2

4 balloons colored; 4



groups.

B. 1 balloon colored; 1




groups.

C. 2 balloons colored; 2

1 balloon colored; 1


Parts of a Number (page 13)

A. 10, 8, 2

B. 6, 6, 8

C. 16, 10, 6

D. 10, 9, 8

E. 14, 15, 12

Improper Fractions and Mixed Numbers(page 14)

A. 32, 1

B. 154, 3

C. 1 , 5

D. 138, 1 58

E. 113, 3 23

F. 136, 2 16

G. 162, 8

H. 124, 3

I. 93, 3

Changing Improper Fractions to MixedNumbers (page 15)

A. 1 , 2, 1 25, 2

B. 3, 5 , 3 , 1 17

C. 2, 2 25, 1 38, 5

D. 8

E. 6

Changing Mixed Numbers to Improper Fractions (page 16)

A. 32, 74, 138, 43

B. 52, 1 , 295, 198

C. 113, 6110, 133, 195

D. Yes, there are enough pieces for 21

students because 30 pieces were cut.

E. 7

Adding and Subtracting Fractions withLike Denominators (page 17)

A. 3 parts colored, ; 2 parts colored, 23; 4

parts colored, 45

B. 5 parts colored, 56; 3 parts colored, 35; 5

parts colored, 58

C. 2 parts crossed out, 25; 1 part crossed

out, 13; 1 part crossed out, 24 or

D. 4 parts crossed out, 38; 4 parts crossed

out, 16; 7 parts crossed out, 210 or 15

E. 57, 29, 710, 26 or 13

F. 79, 110, 67, 910

Adding Fractions with Unlike Denominators (page 18)

A. 56

B. 512

C. 910

D. 78

E. 78

F. 89

G. 710

Answer Key

46

47

H. 712

I. 1112

J. 1516

K. 78

L. 1320

Subtracting Fractions with Unlike Denominators (page 19)

A. 59

B. 512

C. 16

D. 320

E. 38

F. 521

G. 112

H. 18

I. 720

J. 19

K. 512

L. 49

Adding and Subtracting Fractions(page 20)

A.

B. 45

C.

D.

E. 56

F.

G. 13

H. 16

I. 35

J. 58

K. 13

L.

M. 15

N.

O. 1

P. 56

Adding Mixed Numbers (page 21)

A. 4 35, 9 23, 5 78, 11

B. 6 13, 10 47, 11 , 12 18

C. 14 13, 7 23, 8 59, 16 15

Subtracting Mixed Numbers (page 22)

A. 2 49, 1, 13, 3 710

B. 3 , 25, 1, 3 112

C. 5 25, 3 13, 4 16, 6

Problem Solving with Fractions (page 23)

A. 5

B. 10

C. 12

D. 5

E. 24

F. 8

G.

H. 16

Fraction Review (page 24)

A.

B. 59

C. > < < >

D. 36, 28, 26, 48

E. 46, , , 45

F. 13, , ,

G. 3

H. 2

I. 2

J. 6

K. 52, 2

L. 113, 3 23

More Fraction Review (page 25)

A. , 23, 23

B. 1 13, 1, 145

C. , , 58

D. 6 45, 8 15, 7 18, 11

E. 38, 25, 23

F. 112, 18,

G.

H. Suggested answer: Since of 8 pieces

is 2, Sarah ate 2 pieces. Kyle ate 4. That

left 2 pieces, or of 8.

Identifying Tenths (page 26)

A. 310, 0.3, three tenths

B. 210, 0.2, two tenths

C. 610, 0.6, six tenths

D. 410, 0.4, four tenths

E. 810, 0.8, eight tenths

F. 510, 0.5, five tenths

G. 910, 0.9, nine tenths

Identifying Hundredths (page 27)

A. 15100, 0.15

72100, 0.72

50100, 0.50

B. 7100, 0.07

40100, 0.40

8100, 0.08

C. 55 squares should be colored

D. 80 squares should be colored

E. 6 squares should be colored

Decimals Greater Than 1 (page 28)

A. 1 310, 1.3

1 710, 1.7

2 910, 2.9

B. 1 47100, 1.47

2 9100, 2.09

3 65100, 3.65

C. 3.16, 7.5, 9.89, 4.1

Matching Fractions and Decimals(page 29)

A. 310, 410, 910, 17100

B. 1100, 83100, 3100, 110

C. 0.2, 0.7, 0.95, 0.61

D. 0.85, 0.02, 0.46, 0.05

E. 7 710, 12 3100, 5 310, 11 410

F. 8 9100, 4 59100, 6 2100, 15 1100

G. 3.1, 5.7, 10.35, 4.65

H. 9.09, 14.3, 17.1, 7.01

Comparing Tenths (page 30)

For AD, pictures should be colored

accordingly.

A. 0.7

B. 0.9

C. 1.6

D. 1.9

E. < > >

B. <

C. =

D. <

E. =

F. >

G. < = < >

H. > < < >

I. > < =

DTR-Fractions and Decimals 3-4

Documents

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