Fractions - 3plearning.com · For each fraction write a larger fraction below. The new fraction...
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GRADE 4 Fractions WORKSHEETS
Transcript of Fractions - 3plearning.com · For each fraction write a larger fraction below. The new fraction...
GRADE 4
FractionsWORKSHEETS
Grade 4 | FRACTIONS | 4.NF.1 1Copyright © 3P Learning
a
c
b
d
Complete these equivalent fraction models by shading and writing the equivalent fraction:
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.
Label each row of the fraction wall and color each strip a different color. The first one has been done for you.
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
3
2
1 whole
12
12 halves
14
14
14
14
18
18
18
18
18
18
18
18
15
15
15
15
15
110
110
110
110
110
110
110
110
110
110
28
48
210
68
610
24
12
14
15
35
34
12
3
2
1
1
4
5
4
2
8
10
8
8
Grade 4 | FRACTIONS | 4.NF.1 2Copyright © 3P Learning
Here is a fraction wall that has been broken up into pieces. Label the pieces:
c
d
2
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?
First word: A = 24 T = 3
4 L = 15 S = 4
10
Second word: U = 15 H = 8
10 I = 410 W = 1
2 T = 68 O = 2
8
Third word: A = 210 T = 1
5 E = 1 R = 810 W = 1
2
Types of fractions – equivalent fractions
4
5
6
Rewrite these fractions in order from smallest to largest:
4
5
9
10
7
10
2
5
3
10
a b
15
18
110
110
110
110
14
....................2
10
....................48
....................5
10
....................12
....................25
....................15
....................25
....................34
....................2
10
....................68
....................45
....................1010
....................14
....................45
....................2
10
....................34
3Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.1, 4.NF.2
Write either T for true or F for false under each statement:
7
8
Types of fractions – equivalent fractions
a 28 > 1
10
d 45 > 7
10
b 310 < 1
4
e 48 < 3
4
c 35 < 3
10
f 510 < 1
5
Shade and label these models to show equivalent fractions:
a =
=
c =
=
b =
=
d =
=
Grade 4 | FRACTIONS | 4.NF.1 4Copyright © 3P Learning
Circle the correct amounts shown in these fractions:
Show fifths and tenths on these shapes:
Label these fractions:
These fraction strips show fifths and tenths.
1
2
3
Types of fractions – fifths and tenths
110
110
110
110
110
110
110
110
110
110
15
15
15
15
15
a b
a b c
a
d
b
e
c
f
2
3
3
4
6
5
10
10
1
5
5
10
10
10
5
10
Grade 4 | FRACTIONS | 4.NF.1 5Copyright © 3P Learning
Equivalent means they are the same amount.
Color these shapes according to the directions. The equivalent fraction line above will help you.
Place these fractions on the number line: 25 , 1
2 , 310, 7
10, 15
Types of fractions – fifths and tenths
4
5
6
a Color 15 blue and 6
10 red and leave the rest blank.
c Color 35 blue and 2
10 red and leave the rest blank.
b Color 210 orange and 3
5 green and leave the rest blank.
Complete this equivalent fraction number line. The first two have been done for you.
10 10 10 10 10 10 101010
1
10
2
1
5
0 1
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.
0
6Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.3.B
Write the mixed numbers that these fraction models are showing:
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 =
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.
= 210
= 1 210
1
2
a =
c =
b =
d =
7Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.3.B
Complete these number lines:
a
b
c
3
4
Types of fractions – mixed numbers
Shade these fraction models to show the mixed numbers:
a
1 2
5
c
2 2
3
e
2 4
5
b
1 3
4
d
1 4
10
f
1 3
5
012 1 1 1
2 2
015
35
45 1 2
5
014
24
34 1 1 1
4
8Copyright © 3P Learning
a 12 2
8 b 48 3
4 c 26 1
2 d 1012 3
4
Grade 4 | FRACTIONS | 4.NF.2
Rename a fraction in each group so that you can compare them more easily. Circle the largest fraction:
Order these fractions:
1 12 5
4 34 2
4 1 34 1
4 44
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? 34 or 5
8
We know that 34 is equivalent to 6
8 so 34 is larger than 5
8
Hmm … I had better make the mixed numbers into improper fractions as well. That will make them easier to compare.
Write or draw a fraction on the left that would result in the scale looking like this:
1
2
3 × 4
23 = 8
12
× 4
Remember, with equivalent fractions, we think about what we did to get from one to the other:
Grade 4 | FRACTIONS | 4.NF.1 9Copyright © 3P Learning
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:
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.
a Continue cutting the cakes so that each cake has the same number of fair slices:
b If you had one of these new slices, what fraction of the cake would you receive?
Fractions – renaming and ordering fractions
Sometimes we have to order and compare fractions with unrelated denominators, such as 1
4 , 16 , and 1
5 .
To do this, we have to find one common denominator we can convert all the fractions to.
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):12 The multiples of 2 are 2, 4, 6, 8, … 1
3 The multiples of 3 are 3, 6, 9, 12, 15, …
6 is the LCD so we convert both fractions to sixths:
12 =
3
6 13 =
2
6
× 3
× 3
× 2
× 2
× 2 × 3 × 4 × 5 × 62 3 4 5 64 6 8 10 126 9 12 15 188 12 16 20 24
10 15 20 25 3012 18 24 30 3614 21 28 35 4216 24 32 40 4818 27 36 45 54
a 12
14
13
12
b 36
12
13
c 13
14
16
1
2
12
13
Grade 4 | FRACTIONS | 4.NF.1 10Copyright © 3P Learning
For each fraction write a larger fraction below. The new fraction must have a different denominator. It can have a different numerator.
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?
This time, rename the fractions and circle the largest. Underline the smallest.
Fractions – renaming and ordering fractions
12
13
23
45
810
If you can do this, you are a whiz! This is real extension math.
3
4
5
a 12
23
39
b 25
12
13
c 34
23
48
d 34
36
38
a 38
24
56
b 46
12
1112
c 13
58
46
d 34
23
12
11Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.3
a 13 + 2 1
3 =
d 15 + 6 2
5 =
b 2 34 – 1 2
4 =
e 1 312 – 1
12 =
c 1 25 + 3 1
5 =
f 7 412 – 3 2
12 =
Express these as fraction sentences. Solve them:
a Sarah and Rachel go to a salt water taffy stand. Sarah buys 3 1
4 boxes of strawberry taffy and Rachel buys 2 14
boxes of mixed taffy. How much do they buy in total?
b You have 2 34 boxes of chocolates and you eat 1 1
4 boxes. How many boxes do you have left?
c Before World Math Day, Akhil practices Live Mathletics for 4 1
3 hours on Monday and 2 13 hours on Tuesday.
How many hours of practice has he put in altogether?
d Makoa 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?
Solve these problems:
How do we add or subtract fractions? Look at this example:
We had a movie marathon this weekend. On Saturday, we watched movies for 7 14
hours and on Sunday we watched for 5 14 hours. How many hours did we spend
watching movies in total? 7 1
4 + 5 14 =
First we add the whole numbers: 7 + 5 = 12. Then we add the fractions: 14 + 1
4 = 12
Then we add the two answers together: 12 + 12 = 12 1
2We use the same process to subtract fractions.
Calculating – adding and subtracting fractions
1
2
12Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.3
Use renaming to solve these problems. Convert your answers to mixed numbers. You can draw models if that helps:
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 23 + 2 2
3 = which is equivalent to
b 3 24 + 1 3
4 = which is equivalent to
c 7 68 + 5
8 = which is equivalent to
d 3 35 + 16 3
5 = which is equivalent to
Look at this problem: 7 24 + 3 + 3
4
Our answer is 10 54 , which is a little confusing.
54 is the same as 1 1
4 . So let’s add the 1 to our answer of 10. Our answer is now 11 14 .
Sometimes we also come across more complicated subtraction problems.
Look at 1 14 – 3
4 . We can’t take away 34 from 1
4 , so we will need to rename.
1 14 is the same as 5
4 . 54 – 3
4 = 24
a 1 25 – 4
5 =
– =
b 2 24 – 3
4 =
– =
=
c 3 25 – 4
5 =
– =
=
Calculating – adding and subtracting fractions
3
4
13Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.3
Sometimes we need to add and subtract fractions that have different but related denominators.
How do we add 34 + 1
8 ? One way is to use fraction strips to find equivalent fractions.
We can see that 34 is the same as 6
8 68 + 1
8 = 78
Calculating – adding and subtracting fractions
Use the fraction strips above to help you add or subtract the like fractions. Rewrite the fractions in bold:
g Brad ate 26 of a bag of chips. Jen ate 2
3 of a bag of chips. How much did they eat altogether?
5
1
12
12
13
13
13
14
14
14
14
15
15
15
15
15
16
16
16
16
16
16
18
18
18
18
18
18
18
18
110
110
110
110
110
110
110
110
110
110
112
112
112
112
112
112
112
112
112
112
112
112
a 14 +
12
+ =
d 46 +
23
+ =
b 25 +
610
+ =
e 34 –
12
– =
c 45 –
210
– =
f 34 +
18
+ =
14Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.3.D
Jess spent half of her allowance on a magazine. If she gets $10, how much was the magazine?
If one quarter of a package of candies is 8 candies, how many candies are there in the whole package?
Marley and Matt shared a pizza that had been cut into 8 pieces. Marley ate 14 of the
pizza and Matt ate 24 . How many pieces were left?
Amy made 24 cupcakes. She iced 18 of them pink, 2
8 of them blue, and left the rest plain. How many plain cupcakes were there?
Josie ordered two pizzas cut into eighths. If he ate 58 of a pizza, how much was left?
Working with fractions – fraction word problems
1
2
3
4
5
15Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.4
Use repeated addition to multiply these fractions. Show each of the steps:
We can use repeated addition to multiply fractions by whole numbers.
3 × 28 3 sets of two eighths is 2
8 + 28 + 2
8 = 68
3 × 28 = 6
8
Calculating – multiplying fractions by whole numbers
Sam thinks that 6 × 26 is the same as 5 × 2
5 . Is he right? Show how you know:
Try these. Convert your answers to whole numbers:
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 × 38
38 + 3
8 + 38 = 9
24
3 × 3
8 = 924
a 3 × 312
= 312 + 3
12 + 312
=
b 3 × 212 c 5 × 1
8 d 3 × 25
a 6 × 12 b 5 × 2
5 c 8 × 24 d 15 × 3
5
1
2
3
4
16Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.4
Now take your answers from Question 5 and write them here. Divide the numerators by the denominators to find their mixed number equivalents:
Multiply these fractions by whole numbers. Express the answers as improper fractions:
Warm up with these problems. There will be no remainders.
Calculating – multiplying fractions by whole numbers
There is another way to multiply fractions by whole numbers. Look at 3 × 35 .
We have 3 sets of three fifths. We can express this as 3 × 35 = 9
5We don’t multiply the fifths because these don’t change – we still have fifths.
a 4 × 34
4×
=
d 3 × 36
6×
=
b 4 × 23
3×
=
e 2 × 45
5×
=
c 5 × 24
4×
=
f 5 × 23
3×
=
Our answers are all improper fractions. How do we convert these to mixed numbers?
Look at 94 . This is nine quarters.
To change this to a mixed number, we divide the numerator by the denominator:
9 ÷ 4 = 2 with 1 quarter left over. 94 is the same as 2 1
4 .
a 84
÷ =
b 93
÷ =
c 126
÷ =
d 155
÷ =
a =
d =
b =
e =
c =
f =
5
6
7
17Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.4
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
Complete this number line showing equivalent tenths and decimals:
Types of fractions – tenths as decimals
Fractions can be written as decimals. This row of multi-link cubes shows 10 tenths:
610 can be shown like this:
610 as a decimal is 0.6
The decimal point separates the whole number from the decimal.
We would write 1 or 1010 as 1.0
1
2
Ones Tenths0 • 6
0 1
10 10 10 10
0.1
18Copyright © 3P Learning Grade 4 | FRACTIONS | 4.NF.5
Connect the matching fractions and decimals:
Show the place value of these decimals by writing them in the table:
Ones Tenths
a 0.6 •
b 2.7 •
c 5.1 •
Order each set of fractions and decimals from smallest to largest:
a 0.8, 0.2, 410 , 9
10 b 910 , 0.1, 1.0, 5
10
________________________________ _________________________________
Shade the fraction strips so each one matches the fraction or the decimal:
a 0.7
b 410
c 0.5
Fractions and decimals – writing tenths as decimals
1
2
3
4
Tenths are written as decimals like this:
0
110
210
310
410
510
610
710
810
910
1010
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
Ones Tenths3 • 8
The decimal point signals the place value of numbers smaller than 1.This number is 3 and 8
10 or 3 and 0.8.
4
10 0.6
1 210 0.7
6
10 1.2
7
10 0.4
7
10 3.5
4 310 0.9
9
10 4.3
3 510 0.7
