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GRADE 5
Fractions
WORKSHEETS
Fractions and decimals – writing tenths as decimals
1
Label this section of a ruler as centimeters in decimals. The first box has been done for you. (Note: this
diagram has been enlarged so you can see the lines clearly.)
1
2
2
3
These 3 cats were the finalists in the Fattest Cat Competition. Fill in the blanks below:
Felix – 12.2 kg
Leroy – 11.9 kg
Mosley – 11.5 kg
3
a _____________ is heavier than _____________ by 10 of a kilogram.
4
b _____________ is heavier than _____________ by 10 of a kilogram.
7
c _____________ is lighter than _____________ by 10 of a kilogram.
3
Write the mass of each cat and < or > to make the sentence true.
aFelix Leroy
4
bMosley
Felix
The combined mass of which two cats is 23.7 kg?
_________________ and _________________
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Grade 5
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4.NF.6
1
Fractions and decimals – writing tenths as decimals
=
1 whole
=
=
100 hundredths
60
6
is the same amount as
.
100
10
10 tenths
We can divide a whole into one hundred parts. These are called hundredths.
Hundredths are made up of 10 lots of tenths.
5
Show how these amounts are the same:
a
80
8
100 is the same amount as 10 .
20
2
100 is the same amount as 10 .
b
=
c
=
30
3
100 is the same amount as 10 .
70
7
100 is the same amount as 10 .
d
=
6
=
Shade these amounts on the hundred grids:
a
5
10
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b
9
10
Grade 5
c
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10
10
4.NF.6
d
1
10
2
Types of fractions – introducing hundredths
We can divide a whole into one hundred parts.
These are called hundredths.
This hundred grid shows 33 out of 100.
33 .
As a fraction it is
100
=
1 whole
1
Write what part out of 100 the shaded part of the grid shows and record it as a fraction:
a
2
100 hundredths
out of
b
out of
Shade these grids according to the fraction:
26
a
37
c
out of
It is easier to work
out how many squares
not to shade instead
of counting each one.
b
100
75
100
95
d
100
3
c
100
Order the fractions from question 2
from smallest to largest:
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Grade 5
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4.NF.6
3
Types of fractions – hundredths as decimals
This diagram shows 26 hundredths shaded
26 .
or
100
Fractions can be written as decimals.
As a decimal, this amount is written as:
Ones
0
1
Label each hundredth grid picture with the fraction and decimal:
a
2
•
Tenths
Hundredths
2
6
10 is the same
100
as 1 which is
10
the same as 0.1
b
Color this grid of stars according to the directions below:
22
aOrange100
bBlue
12
100
9
cGreen 100
dPink
25
100
eYellow 0.15
fRed
0.17
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Grade 5
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4
Fractions and decimals – relating tenths, hundredths, and decimals
Fractions can be written as decimals.
As a decimal, this amount is written as:
This diagram shows 26 hundredths shaded
26 .
or
100
Ones
0
1
Tenths
Hundredths
2
6
•
Complete this table to show the amounts as tenths, hundredths, and decimals:
aTenths
bTenths
Hundredths
Hundredths
Decimal
Decimal
cHundredths
1.5 is same as 1.50.
Decimal
dHundredths
Decimal
2
Show the place value of these decimals by writing them in the table:
Hundreds
Tens
Ones
Tenths
a
2.6
•
b
3.76
•
c
112.6
•
d
45.67
•
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Grade 5
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4.NF.6
Hundredths
5
Fractions and decimals – relating tenths, hundredths, and decimals
3
Shade the fractions on the grid and show them as hundredths and decimals:
1
2
a
1
4
b
= 0.
=
100
100
1
5
c
1
10
d
= 0.
=
100
Express these common fractions as hundredths and as decimals:
1
a 2 =
3
d 4 =
5
= 0.
=
100
4
= 0.
=
100
100
= 0.
4
b 5 =
= 0.
2
e 4 =
100
100
= 0.
4
c 10 =
100
= 0.
5
f 10 =
100
= 0.
= 0.
Show where the decimals fit on the number lines:
a 0.5
0.25
0.8
0
b 1.5
1
1.25
1.75
1
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2
Grade 5
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4.NF.6
6
Fractions – simplifying fractions
1 2 6
75 3,455
These fractions are all equivalent to one half: 2 4 12 150 6,910
1
Which is the simplest? 2
A fraction is in its simplest form when 1 is the only number that both numbers can be divided by.
We simplify fractions to make reading and working with fractions easier.
1
Circle the simplest fraction in each group:
a
1
2
2
4
50
100
b
33
99
3
9
1
3
c
25
100
1
4
5
20
d
2
3
6
9
16
24
To find the simplest fraction, we divide both the numerator and the denominator by the same number.
It makes sense for this to be the biggest number we can find so we don’t have to keep dividing.
This number is called the Greatest Common Factor (GCF).
Look at:
1
? What is the biggest number that goes into both 6 and 18?
6 ÷6
6
=
=
18 ÷ 6
18
3
6 is the biggest number that goes into 18 and 6.
?
2
3
Find the greatest common factor and then simplify:
15
a 20 GCF is
15 ÷
 20 ÷
=
9
b 30 GCF is
9 ÷
 30 ÷
=
16
c 24 GCF is
16 ÷
 24 ÷
=
12
d 36 GCF is
12 ÷
 36 ÷
=
Wally says he has simplified these fractions as far as he can. Is he right? If not, find the simplest fraction:
16
8
a 20  10
50
25
5
b 100  50  10
24
4
c 36  6
15
3
d 20  4
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Grade 5
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5.NF.1
7
Fractions – simplifying fractions
4
Write the following fractions in their simplest form:
28
a
=
49
e
5
12
b
=
20
32
=
36
f
9
=
15
24
c
=
42
16
=
48
g
If you are not
sure what the GCF
is, guess, check,
and improve is a
useful strategy. Try
your choice out
and then look at
your new fraction.
13
d
=
39
h
15
=
55
Could it be any
simpler? Is 1 the
ONLY number that
could go into both
the numerator and
the denominator?
Solve the following problems. Write your answers in the simplest form:
16
a Luke scored 20 on a test. What fraction was incorrect?
12
b Marika scored 20 on the same test. What fraction did she get right?
c25 out of the 75 kids in 6th grade ride their bikes to school.
What fraction does this represent?
dOut of the 26 students in 6F, 14 rate math as their favorite subject.
What fraction is this?
e What fraction did not choose math as their favorite subject?
6
Color and match the fractions on the bottom row with their simplest form:
1
2
2
3
3
5
1
9
1
4
3
4
15
20
25
100
9
81
60
100
12
18
40
80
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Grade 5
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5.NF.1
8
Improper fractions and mixed numbers
An improper fraction has a bigger numerator (top) than denominator (bottom).
3
5
Improper fractions
2
4
numerator 2denominator
Mixed numbers have a whole number and a proper fraction.
Mixed numbers
11
11
2
4
a “mix” of whole numbers and proper fractions
Mixed numbers are simplified improper fractions.
Simplify these:
Improper fractions to mixed numbers
(i) 5
3
5 = 5'3
3
numerator
= numerator 'denominator
denominator
= 1r 2
Whole number answer
= 12
3
remainder
same denominator
14 = 7 = 7 ' 2 Simplify if possible
4
2
(ii) 14
picture form
= 3r1
4
1
= 32
Whole number answer
remainder
same simplified denominator
Mixed numbers to improper fractions
+
(i) 1 2
3
1
#
2 = 3 # 1+ 2
3
3
= 5
same denominator
3
+
(ii)2 1
5
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2
#
1 = 5 #2+1
5
5
same denominator
= 11
5
Grade 5
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4.NF.6
9
Improper fractions and mixed numbers
1
Write the mixed numbers represented by these shaded diagrams:
a
=
b
=
c
=
d
=
e
=
f
=
Make sure you write the fraction in simplest form where possible.
2
Simplify these improper fractions by writing them as mixed numbers.
a 12
5
3
9
2
b 21
c 18
14
16
Write the equivalent improper fraction for these mixed numbers.
a 1 1
2
5
c 23
3
Write these fractions in simplest form first, then change to mixed numbers.
a 15
4
b 14
c 4 4
b 2 3
5
4
Write the equivalent improper fraction for these mixed numbers after first simplifying the fraction parts.
a 4 2
12
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b 2 6
c 25 24
24
Grade 5
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4.NF.6
10
Adding and subtracting fractions with the same denominator
1
Simplify these without the aid of a calculator:
a 1 + 1
b 3 - 1
c 5 + 2
d 8 - 6
e 11 - 4
f 3 + 5
3
11
2
5
11
15
9
15
8
9
8
a 1 + 4
b 8 - 2
c 2 + 5
d 10 - 1
e 11 + 4
f 15 - 8
4
2
5
4
5
7
3
7
2
3
2
Simplify these without the aid of a calculator, remembering to write the answer in simplest form:
a 11 - 5
4
4
5
Simplify these without the aid of a calculator:
2
3
3
b 13 + 19
4
6
c 9 + 13
6
8
8
Simplify these without the aid of a calculator:
a 4 + 1 + 2
b 20 - 10 - 4
c 1 + 1 - 1
d 1 + 4 - 2
e 8 - 4 + 6
f 13 + 11 - 9
9
5
9
5
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9
5
3
7
Grade 5
3
7
3
2
7
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6
5.NF.1
2
2
6
6
11
Adding and subtracting fractions with a different denominator
+
=
1
4
+
1
2
=
?
one quarter
and
one half
equals
?
+
1#2 = 2
4
2#2
=
3
4
1
4
+
2
4
=
one quarter
and
two quarters
equals
three quarters
Simplify these expressions, which have fractions with different denominators:
22
11
(i) 2 + 1 For
and
3
3
55
3 5
Denominators are different
2 + 1 = 2 #5 + 1#3
3 5
3#5 5#3
Multiply top and bottom by
the number used to make the
denominator equal to the LCM
(ii) 7 - 1 + 3 8
2
4
The LCM of the denominators is 15
= 10 + 3
15 15
Equivalent fractions with LCM denominators
= 10 + 3
15
Add the numerators only
= 13
15
For 7 , 1 , and 3
8 2
Denominators are all different
4
7 - 1 + 3 = 7 - 1#4 + 3#2
8 2 4
8 2#4 4#2
= 7-4+6
8 8 8
The LCM of all the denominators is 8
Equivalent fractions with LCM in the denominators
= 7- 4+ 6
8
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= 9
8
Simplify the numerator
= 11
8
Simplify to mixed number
Grade 5
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4.NF.6
12
Adding and subtracting fractions with a different denominator
1
Fill in the spaces for these calculations:
a 1 + 1 The LCM of the denominators is:
3
b 4 - 1 The LCM of the denominators is:
6
1 1
1#
3 + 6 = 3#
=
7
5
5 - 1 = 5#
7 5
7#
1
+6
+1
6
=
=
=
2
=
- 51 ## 77
-
simplest form
simplest form
Simplify these without the aid of a calculator:
a 1 + 1
b 5 - 1
c 2 - 1
d 1 + 3
e 6 - 2
f 3 + 3
3
5
7
2
6
4
6
3
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5
Grade 5
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2
4
8
4.NF.6
13
Adding and subtracting fractions with a different denominator
3
Simplify these expressions without the aid of a calculator, remembering to write the answer in simplest form.
a 1 + 4
2
b 13 - 3
5
8
5
c 1 + 3 - 1
d 3 + 3 - 3
e 2 - 1 + 5
f
2
3
8
4
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4
5
6
Grade 5
10
4
7 - 1 + 11
12 3 24
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14
Adding and subtracting fractions with a different denominator
The same rules apply for questions with a mix of whole numbers and fractions. Here are some examples:
Simplify these expressions, which have a mix of whole numbers and fractions:
(i) 3 + 1 3+ 1 = 3 1
4
4
Write the fraction after the whole number
Write the whole number as a fraction with same denominator
(ii) 1 - 2
1- 2 = 5 - 2
5
5 5
= 3
5
4 - 2 = 28 - 2
7
7
7
= 26
7
= 35
7
Write the whole number as a fraction with same denominator
4
5
(iii) 4 - 2
7
4
Subtract the numerators only
Simplify the fraction
Simplify these expressions:
a 2 + 1
b 1 + 3
c 1 - 2
d 1 - 3
e 2 - 3
f 4 - 1
g 3 - 5
h 5 - 5
2
4
3
8
5
4
3
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2
Grade 5
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4.NF.6
15
Multiplying and dividing fractions
To multiply fractions, just remember: Multiply the numerators (top) and the denominators (bottom).
of = “ # ”
1 of 2 = 1
3
5
3
#
2 = 1#2 = 2
5
15
3#5
To divide an amount by a fraction, just remember: flip the second fraction, then multiply.
1 '2 = 1
3 5
3
#
5
2
Flip only the second fraction.
= 1#5
3#2
Change the “'” to a “ # ”
= 5
6
Simplify these:
Remember: A flipped fraction
is called the reciprocal fraction.
We can use shaded diagrams to calculate the multiplication of two fractions.
(i) 2 of 4 3
Draw a grid using the denominators as the dimensions
3
5
5
4
2
3
Use the numerators to shade columns/rows
5
= 8
15
2
3
#
4 = 8
5
15
Write where they overlap as a fraction
If whole numbers are involved, write them as a fraction.
(ii) 28 '
2
7
28 ' 2
7
= 28 # 7
2
= 28 # 7
1
2
= 196
2
= 98
1
Flip the second fraction and change the sign to “ # ”
Write the whole number as a fraction
Simplify
= 98
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Grade 5
| FRACTIONS |
5.NF.4
16
Multiplying and dividing fractions
1
Calculate these fraction multiplications by shading the given grids:
a
1 of 3
5
4
b
2 of 4
3
7
3
5
7
4
2 of 4
=
3
7
1 of 3 =
5
4
c
4 of 4
5
5
d
5
2 of 3
5
8
5
5
8
2 of 3 =
5
8
4 of 4 =
5
5
=
simplified
e
3 of 7
4
9
f
3 of 5
4
6
4
4
9
3 of 7 =
4
9
6
3 of 5 =
4
6
=
simplified
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Grade 5
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=
simplified
4.NF.6
17
Operations with mixed numbers
Just change to improper fractions, then use the same methods as shown earlier.
Simplify these calculations involving mixed numbers:
Addition and subtraction
(i) 1 2 + 2 1
3
6
1 2 + 2 1 = 5 + 13
3
3
6
6
= 10 + 13
6
6
Change to improper fractions
Equivalent fractions with LCM denominators
= 23
6
= 35
6
Or just add the whole numbers
and the fractions separately.
1+ 2 = 3 2 + 1 = 5
3
6
6
(ii) 4 1 - 1 1
5
2
Simplify to mixed number
4 1 - 1 1 = 21 - 3
5
2
5
2
= 42 - 15
10 10
Change to improper fractions
Equivalent fractions with LCM denominators
= 27
10
= 2 7
10
Simplify to mixed number
Multiplication and division
(iii) 1 3 # 2 1
4
3
(iv) 1 1 ' 2
6
13
4
#2
1 = 7
4
3
2 = 2 , 3 = 3 , etc.
1
1
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7
3
Change to improper fractions
= 49
12
Multiply tops and bottoms together
= 4 1
12
Simplify to mixed number
1 1 '2 = 7 ' 2
6
6 1
= 7
6
Remember
#
#
= 7
12
Grade 5
1
2
Change to improper fractions
Flip second fraction and multiply
Multiply numerators and denominators together
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4.NF.6
18
Word problems with fractions
While on a shopping trip, Xieng spent two-fifths of her money on clothes and one-third on cosmetics.
What fraction of her money did Xieng have left?
2 + 1 = fraction of Xieng’s money spent on shopping
5 3
= 6+ 5
15
Add the numerators together
= 11
15
15 - 11 = 4
15 15
15
Fraction for all of Xieng’s money
Fraction spent
Fraction of money Xieng has left
Xieng still has 4 of her money after shopping
15
Here are some other word problem examples:
(i)In a group of eighteen friends, one-third are girls and one-sixth of these girls have blonde hair. How many
blonde girls are in the group?
1 of 1 of 18 = number of blonde girls in the group
6
3
= 1 # 1 # 18
6 3 1
= 18
18
= 1
There is 1 blonde girl in the group of friends.
(ii)During one night, possums ate two-fifths of the fifty-five fruits on a tree. If one-eleventh of the eaten fruits
grew back, how many fruits are now on the tree?
2
5
# 55
= Number of fruits eaten
= 110
5
= 22
1
11
# 22
= Number of fruits that grew back
= 22
11
= 2
Number of fruits now on the tree
= 55 - 22 + 2
= 35 pieces of fruit
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Grade 5
| FRACTIONS |
5.NF.2
19
Word problems with fractions
1
At a recent trivia night, one table of competitors answered five-eighths of the fifty-six questions correctly. How
many questions did they get incorrect?
2
Co Tin usually takes approximately sixty and one-quarter steps every minute when walking. How many steps
does he expect to take when he exercises by walking for one and two-third hours each day?
3
A vegetable garden has one-third carrots, one-sixth pumpkins, one-quarter herbs. The rest are potato plants.
How many potato plants are in this garden of eighty plants?
4
A class of twenty-four students compared eye colors on a chart. Two-thirds of the class had brown eyes, and threeeighths of those brown-eyed students were boys. How many girls had brown eyes?
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Grade 5
| FRACTIONS |
4.NF.6
20
Word problems with fractions
5
For one particular school: There are 256 students in Grade 7. Grades 8, 9, and 10 all have half the number of
students as the year just below them. How many students are there at this school in Grades 7 to 10?
6
Five-sevenths of the fifty-six images used as backgrounds on Meagan’s touchpad were photos she took herself.
After five-eighths of these photos were deleted, what fraction of the background images now are not photos
taken by her?
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Grade 5
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4.NF.6
21
Summary of the things you need to remember for fractions
Proper fractions
Represent parts of a whole number or object. The numerator is smaller than or equal to the denominator.
numerator
denominator
number of equal parts you have
total number of equal parts
1
2
Equivalent proper fractions
These are fractions with different numbers that represent the same amount.
4 = 2 = 1 = Equivalent
4
2
8
fractions
Improper fractions and mixed numbers
3
2
5
4
Improper fractions
11
2
numerator > denominator
Mixed numbers
11
4
A “mix” of whole numbers and proper fractions.
Fractions on the number line
0
1
1
2
3
4
31
2
Start
number of equal steps taken between 0 and 1
total number of equal steps between 0 and 1
number of equal steps towards the next whole number
total number of equal steps between start and next whole number
Reciprocal fractions
2
5
Original fraction
31
2
Mixed number
7
2
7
2
5
2
Reciprocal fraction
2
Reciprocal fraction
7
Comparing fractions
Write equivalent fractions by changing the denominators to their LCM, then compare the numerators
1#3
2#3
3
6
2
2
6
1#2
3#2
Adding and subtracting fractions
If the denominators (bottom) are the same, then simply add or subtract the numerators (top).
If the denominators are different, change to equivalent fractions with the same denominators using the LCM. Then add
or subtract the numerators of the new fractions.
Multiplying and dividing fractions
To multiply fractions, just remember: Multiply the numerators (top) and the denominators (bottom).
To divide an amount by a fraction, just remember: flip the second fraction (reciprocal), then multiply.
“of” means “ # .” Find 2 of 2 means calculate 2 # 2
Fractions of an amount
5
5
Two amounts as a fraction
2 out of 5 as a fraction is 2 . If the two amounts are in different units, change the larger amount into the smaller units.
5
So 200 g out of 2 kg becomes 200 g out of 2,000 g.
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Grade 5
| FRACTIONS |
4.NF.6
22