GRADE 4
Fractions
WORKSHEETS
Types of fractions – equivalent fractions
This fraction wall shows fractions that are equivalent. Equivalent fractions are
fractions that are the same amount. How many equivalent fractions can you find?
1
Label each row of the fraction wall and color each strip a different color. The first one
has been done for you.
1 whole
1
8
1
10
2
1
4
1
5
1
2
1
8
1
10
1
8
1
5
1
10
1
10
1
8
1
10
1
8
1
5
1
10
1
4
1
8
1
5
1
10
halves
1
4
1
8
1
10
1
10
1
5
1
8
1
10
Match the fractions in the top row with the equivalent fractions underneath by
drawing a line to connect them. The first one has been done for you.
1
2
1
4
2
8
3
1
4
1
2
1
5
4
8
3
5
2
10
3
4
6
8
1
2
6
10
2
4
Complete these equivalent fraction models by shading and writing the equivalent fraction:
a
c
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3
4
2
5
8
10
Grade 4
1
b
4
1
d
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4.NF.1
8
8
1
Types of fractions – equivalent fractions
4
5
Rewrite these fractions in order from smallest to largest:
4
9
7
2
3
5
10
10
5
10
Here is a fraction wall that has been broken up into pieces. Label the pieces:
1
5
a
c
1
10
1
10
1
10
1
8
1
10
1
4
d
6
b
Match the equivalent fractions to find out an interesting animal fact:
Q: What is something that a rat can do for longer than a camel?
2
3
1
4
T = 4
L = 5
S = 10
First word: A = 4 1
8
4
1
6
2
T = 8 O = 8
Second word: U = 5 H = 10 I = 10 W = 2 2
1
8
1
E = 1
R = 10 W= 2
Third word: A = 10 T = 5 .................... .................... .................... ....................
2
10
1
2
2
5
6
8
.................... .................... .................... .................... .................... .................... ....................
4
8
2
5
3
4
4
5
1
4
2
10
3
4
.................... .................... .................... .................... ....................
5
10
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1
5
2
10
Grade 4
10
10
4
5
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4.NF.1
2
Types of fractions – equivalent fractions
7
8
Shade and label these models to show equivalent fractions:
a
=
b
=
=
=
c
=
d
=
=
=
Write either T for true or F for false under each statement:
2
a 8
>
1
10
4
d 5
3
b 10
<
1
4
3
c 5
>
7
10
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3
10
<
1
5
4
e 8
<
3
4
5
f 10
Grade 4
<
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4.NF.1, 4.NF.2
3
Types of fractions – fifths and tenths
These fraction strips show fifths and tenths.
1
5
1
10
1
1
5
1
10
1
10
1
10
1
10
1
10
1
5
1
10
1
10
1
10
b
c
Show fifths and tenths on these shapes:
a
d
3
1
10
1
5
Label these fractions:
a
2
1
5
2
5
3
10
5
b
10
10
e
10
c
f
4
5
6
10
Circle the correct amounts shown in these fractions:
a
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3
10
Grade 4
1
b
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4
Types of fractions – fifths and tenths
4
Complete this equivalent fraction number line. The first two have been done for you.
1
2
10
10
0
Equivalent means
they are the
same amount.
10
10
10
10
10
10
10
10
1
5
5
2 1 3 7 1
Place these fractions on the number line: 5 , 2 , 10 , 10 , 5
0
6
1
Color these shapes according to the directions. The equivalent fraction line above will
help you.
1
6
2
3
bColor 10 orange and 5 green and
aColor 5 blue and 10 red and leave
the rest blank.
leave the rest blank.
3
2
cColor 5 blue and 10 red and leave
the rest blank.
If a shape is divided into fifths, I need
to change the fractions to fifths.
If a shape is divided into tenths, I need
to change the fractions to tenths.
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Grade 4
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4.NF.1
5
Types of fractions – mixed numbers
A mixed number is a whole number and a fraction. For example, say we connected
10 multi-link cubes and named this as 1 whole.
= 1
If we then picked up 2 more multi-link cubes we have another 2 tenths.
2
= 10
2
= 1 10
1
2
In each of these problems, 10 multi-link cubes represent 1 whole. Write the mixed
number for each set of multi-link cubes.
a
=
b
=
c
=
Write the mixed numbers that these fraction models are showing:
a
=
b
=
c
=
d
=
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Grade 4
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4.NF.3.B
6
Types of fractions – mixed numbers
3
Shade these fraction models to show the mixed numbers:
b
a
2
15
c
d
2
23
4
1 10
e
f
4
25
4
3
14
3
15
Complete these number lines:
a
b
c
1
2
0
0
1
4
0
1
5
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1
12
1
2
4
2
3
4
1
3
5
4
5
Grade 4
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1
14
2
15
4.NF.3.B
7
Fractions – comparing and ordering fractions
Comparing and ordering fractions with like denominators is a simple process:
When there are different denominators we need to rename the fractions so they
have the same denominators. This lets us compare apples with apples.
Which is larger?
3
3
5
4 or 8
6
3
5
We know that 4 is equivalent to 8 so 4 is larger than 8
1
Order these fractions:
1
12
2
3
4
2
4
3
14
1
4
4
4
Rename a fraction in each group so that you can compare them more easily. Circle the
largest fraction:
1
a 2
3
5
4
Hmm … I had
better make
the mixed
numbers into
improper
fractions as
well. That will
make them
easier to
compare.
2
8
4
b 8
3
4
2
c 6
Write or draw a fraction on the left that would result in
the scale looking like this:
1
2
10
d 12
3
4
Remember, with × 4
equivalent fractions,
we think about what 2 = 8
3 12
we did to get from one to the other: × 4
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Grade 4
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4.NF.2
8
Fractions – renaming and ordering fractions
Sometimes we have to order and compare fractions with unrelated denominators,
1 1
1
such as 4 , 6 , and 5 .
To do this, we have to find one common denominator we can convert all the
fractions to.
You have 2 cakes for a class party. One has been cut into halves and one into thirds.
The problem is that you want each slice to be an equal fraction of the cakes.
1
aContinue cutting the cakes
so that each cake has the
same number of fair slices:
1
2
1
3
b If you had one of these new slices, what fraction of the cake would you receive?
That is an example of how we rename fractions. We find a way to re-divide the wholes
so that they have the same number of parts. To do this efficiently we find the
smallest shared multiple. This is then called the Lowest Common Denominator (LCD):
1 The multiples of 2 are 2, 4, 6, 8, … 1 The multiples of 3 are 3, 6, 9, 12, 15, …
2
3
6 is the LCD so we convert both fractions to sixths:
1
2
2
×3
3
×3
6
=
1
3
×2
2
×2
6
=
Rename these fractions by first finding the shared LCD and
then converting the fractions. Use the multiplication table on
the right to help you find the LCD:
a
1
2
12 1
4
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1
3
3
b 6 1
2
Grade 4
1
3
c
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1
3
1
4
4.NF.1
1
6
×2
2
4
6
8
10
12
14
16
18
×3
3
6
9
12
15
18
21
24
27
×4
4
8
12
16
20
24
28
32
36
×5
5
10
15
20
25
30
35
40
45
×6
6
12
18
24
30
36
42
48
54
9
Fractions – renaming and ordering fractions
3
Look at each group of fractions. Predict which you think is the largest and circle your
prediction. Now, rename the fractions in the work space below so that each fraction in
the group has the same denominator. Use a different color to circle the largest fraction.
Are there any surprises?
a
1
2
4
3
9
2
b 5 1
2
1
3
c
3
4
2
3
4
8
3
d 4 3
6
3
8
This time, rename the fractions and circle the largest. Underline the smallest.
a
3
8
5
2
3
2
4
5
6
4
b 6 1
2
11
12
c
1
3
5
8
4
6
3
d 4 2
3
1
2
For each fraction write a larger fraction below. The new fraction must have a different
denominator. It can have a different numerator.
1
2
1
3
2
3
4
5
8
10
If you can do this, you
are a whiz! This is real
extension math.
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Grade 4
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Calculating – adding and subtracting fractions
How do we add or subtract fractions? Look at this example:
1
We had a movie marathon this weekend. On Saturday, we watched movies for 7 4
1
hours and on Sunday we watched for 5 4 hours. How many hours did we spend
watching movies in total?
1
1
74 + 54 =
1
1
1
First we add the whole numbers: 7 + 5 = 12. Then we add the fractions: 4 + 4 = 2
1
1
Then we add the two answers together: 12 + 2 = 12 2
We use the same process to subtract fractions.
1
2
Solve these problems:
1
1
a 3 + 2 3 =
3
2
b 2 4 – 1 4 =
2
1
c 1 5 + 3 5 =
1
2
d 5 + 6 5 =
3
1
e 1 12 – 12 =
4
2
f 7 12 – 3 12 =
Express these as fraction sentences. Solve them:
aSarah and Rachel go to a salt water taffy stand. Sarah
1
1
buys 3 4 boxes of strawberry taffy and Rachel buys 2 4
boxes of mixed taffy. How much do they buy in total?
3
1
bYou have 2 4 boxes of chocolates and you eat 1 4
boxes. How many boxes do you have left?
cBefore World Math Day, Akhil practices Live Mathletics
1
1
for 4 3 hours on Monday and 2 3 hours on Tuesday.
How many hours of practice has he put in altogether?
dMakoa has five and a half shelves of old sports
equipment. His mother makes him take some of it
to the local thrift store. This leaves him with 2 full
shelves. How much has he taken to the store?
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Grade 4
| FRACTIONS |
4.NF.3
11
Calculating – adding and subtracting fractions
2
3
Look at this problem: 7 4 + 3 + 4
5
Our answer is 10 4 , which is a little confusing.
5
1
1
4 is the same as 1 4 . So let’s add the 1 to our answer of 10. Our answer is now 11 4 .
3
Solve these problems, converting any improper fractions in your answer to mixed
numbers. You can use the models to help you with the renaming:
a
2
2
3 + 23
=
which is equivalent to
b
2
3
34 + 14 =
which is equivalent to
c
6
5
78 + 8
=
which is equivalent to
d
3
3
3 5 + 16 5 =
which is equivalent to
Sometimes we also come across more complicated subtraction problems.
1
3
3
1
Look at 1 4 – 4 . We can’t take away 4 from 4 , so we will need to rename.
1
5
5
3
2
–
=
4
4
4
1 4 is the same as 4 .
4
Use renaming to solve these problems. Convert your answers to mixed numbers.
You can draw models if that helps:
2
4
2
3
2
4
a1 5 – 5 =
b2 4 – 4 =
c3 5 – 5 =
–
=
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Grade 4
–
=
=
| FRACTIONS |
4.NF.3
–
=
=
12
Calculating – adding and subtracting fractions
Sometimes we need to add and subtract fractions that have different but related
denominators.
3
1
How do we add 4 + 8 ? One way is to use fraction strips to find equivalent fractions.
3
6
6
1
7
We
can
see
that
is
the
same
as
+
=
4
8
8
8
8
1
1
2
1
2
1
3
1
3
1
4
1
4
1
5
1
6
5
1
8
1
10
1
10
1
12
1
12
1
5
1
6
1
8
1
5
1
6
1
8
1
10
1
12
1
4
1
5
1
6
1
8
1
12
1
4
1
5
1
10
1
3
1
8
1
10
1
12
1
6
1
8
1
10
1
12
1
12
1
6
1
8
1
10
1
12
1
8
1
10
1
12
1
10
1
12
1
10
1
12
1
12
Use the fraction strips above to help you add or subtract the like fractions. Rewrite the
fractions in bold:
1
1
2
6
4
2
a 4 + 2
b 5 + 10
c 5 – 10
d
+
4
6
+
=
2
3
+
e
=
+
3
4
–
–
=
1
2
f
=
–
3
4
+
+
=
1
8
=
2
2
gBrad ate 6 of a bag of chips. Jen ate 3 of a bag of chips. How much did they eat
altogether?
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Grade 4
| FRACTIONS |
4.NF.3
13
Working with fractions – fraction word problems
1
Jess spent half of her allowance on a magazine. If she gets $10, how much was
the magazine?
2
If one quarter of a package of candies is 8 candies, how many candies are there in the
whole package?
3
1
Marley and Matt shared a pizza that had been cut into 8 pieces. Marley ate 4 of the
2
pizza and Matt ate 4 . How many pieces were left?
4
1
2
Amy made 24 cupcakes. She iced 8 of them pink, 8 of them blue, and left
the rest plain. How many plain cupcakes were there?
5
5
Josie ordered two pizzas cut into eighths. If he ate 8 of a pizza, how much was left?
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Grade 4
| FRACTIONS |
4.NF.3.D
14
Calculating – multiplying fractions by whole numbers
We can use repeated addition to multiply fractions by whole numbers.
2
2
3 × 8
2
2
6
3 sets of two eighths is 8 + 8 + 8 = 8
2
6
3 × 8 = 8
1
Use repeated addition to multiply these fractions. Show each of the steps:
3
a 3 × 12
3
3
3
= 12 + 12 + 12
2
b 3 × 12
1
c 5 × 8
2
d 3 × 5
=
2
Try these. Convert your answers to whole numbers:
1
a 6 × 2
3
4
2
b 5 × 5
2
c 8 × 4
3
d 15 × 5
2
2
Sam thinks that 6 × 6 is the same as 5 × 5 . Is he right? Show how you know:
Sam’s dad helped him with his homework. Here is what his dad did. Is he right?
If not, explain to him where he went wrong.
3
3 × 8
3
3
3
9
+ 8 + 8 = 24
8
3
9
3 × 8 = 24
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Grade 4
| FRACTIONS |
4.NF.4
15
Calculating – multiplying fractions by whole numbers
3
There is another way to multiply fractions by whole numbers. Look at 3 × 5 .
3×3
9
We have 3 sets of three fifths. We can express this as 5 = 5
We don’t multiply the fifths because these don’t change – we still have fifths.
5
Multiply these fractions by whole numbers. Express the answers as improper fractions:
3
2
2
a 4 × 4
b 4 × 3
c 5 × 4
×
×
×
=
=
=
4
3
4
3
d 3 × 6
×
6
4
e 2 × 5
×
5
=
2
f 5 × 3
×
3
=
=
Our answers are all improper fractions. How do we convert these to mixed numbers?
9
Look at 4 . This is nine quarters.
To change this to a mixed number, we divide the numerator by the denominator:
9
1
9 ÷ 4 = 2 with 1 quarter left over. 4 is the same as 2 4 .
6
Warm up with these problems. There will be no remainders.
a
7
8
4
b
÷
=
9
3
c
÷
=
12
6
d
÷
=
15
5
÷
=
Now take your answers from Question 5 and write them here. Divide the numerators
by the denominators to find their mixed number equivalents:
a
=
b
=
c
=
d
=
e
=
f
=
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Grade 4
| FRACTIONS |
4.NF.4
16
Types of fractions – tenths as decimals
Fractions can be written as decimals.
This row of multi-link cubes shows 10 tenths:
6
10 can be shown like this:
Ones
Tenths
6
0
•
6
10 as a decimal is 0.6
The decimal point separates the whole number from the decimal.
10
We would write 1 or 10 as 1.0
1
Complete this number line showing equivalent tenths and decimals:
10
10
10
10
0
1
0.1
2
If a row of 10 multi-link cubes is 1 whole, then label the other rows with a fraction
and decimal:
Fraction Decimal
a
b
c
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Grade 4
| FRACTIONS |
4.NF.4
17
Fractions and decimals – writing tenths as decimals
Tenths are written as decimals like this:
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
Shade the fraction strips so each one matches the fraction or the decimal:
a 0.7
b
4
10 c 0.5
2
Order each set of fractions and decimals from smallest to largest:
4 9
9
5
b 10 , 0.1, 1.0, 10
a 0.8, 0.2, 10 , 10 __________________________________________________________________
3
Show the place value of these decimals by writing them in the table:
Ones
4
Tenths
a
0.6
•
b
2.7
•
c
5.1
•
Connect the
matching fractions
and decimals:
Copyright © 3P Learning
Ones
3
•
Tenths
8
The decimal point signals the place
value of numbers smaller than 1.
This number is 3 and 8 or 3
10
and 0.8.
4
10 2
1 10 6
10 7
10 Grade 4
7
10 3
4 10 9
10 5
3 10 0.6
0.7
1.2
0.4
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4.NF.5
3.5
0.9
4.3
0.7
18