ID : ae-4-Convert-Mixed-to-Improper-Fraction [1]
Grade 4
Convert Mixed to Improper Fraction
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(1) Write the following fractions in the simplest form:
A) B)
8
20
= .
72
171
=
D)
22
33
=
G)
9
27
=
J)
36
80
=
M)
6
24
=
.
.
.
.
E)
11
220
=
H)
120
152
=
K)
56
63
=
N)
60
144
=
.
.
.
.
.
C)
32
72
=
F)
7
77
=
I)
8
16
=
L)
44
55
=
O)
12
36
=
.
.
.
.
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [2]
Answers
(1) A)
2 5
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
8
20
in the simplest/lowest form, let us find the HCF of
8 and 20:
2 | 8
2 | 4
2 | 2
| 1
Factors of 8 = 2 × 2 × 2
2 | 20
2 | 10
5 | 5
| 1
Factors of 20 = 2 × 2 × 5
The HCF of 8 and 20 is 2 × 2 = 4 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
8
20
by its
HCF 4 in order to bring it into its simplest/lowest form:
8
20
=
8 ÷ 4
20 ÷ 4
=
2
5
Step 5
Hence, the simplest/lowest form of
8
20
is
2
5
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [3]
B)
8 19
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
72
171
in the simplest/lowest form, let us find the HCF of 72 and 171:
2 | 72
2 | 36
2 | 18
3 | 9
3 | 3
| 1
Factors of 72 = 2 × 2 × 2 × 3 × 3
3 | 171
3 | 57
19 | 19
| 1
Factors of 171 = 3 × 3 × 19
The HCF of 72 and 171 is 3 × 3 = 9 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
72
171
by its
HCF 9 in order to bring it into its simplest/lowest form:
72
171
=
72 ÷ 9
171 ÷ 9
=
8
19
Step 5
Hence, the simplest/lowest form of
72
171
is
8
19
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [4]
C)
4 9
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
32
72
in the simplest/lowest form, let us find the HCF of
32 and 72:
2 | 32
2 | 16
2 | 8
2 | 4
2 | 2
| 1
Factors of 32 = 2 × 2 × 2 × 2 × 2
2 | 72
2 | 36
2 | 18
3 | 9
3 | 3
| 1
Factors of 72 = 2 × 2 × 2 × 3 × 3
The HCF of 32 and 72 is 2 × 2 × 2 = 8 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
32
72
by its
HCF 8 in order to bring it into its simplest/lowest form:
32
72
=
32 ÷ 8
72 ÷ 8
=
4
9
Step 5
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [5]
Hence, the simplest/lowest form of
32
72
is
4
9
.
D)
2 3
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
22
33
in the simplest/lowest form, let us find the HCF of
22 and 33:
2 | 22
11 | 11
| 1
Factors of 22 = 2 × 11
3 | 33
11 | 11
| 1
Factors of 33 = 3 × 11
The HCF of 22 and 33 is 11.
Step 4
Now, let us divide both the numerator and denominator of the fraction
22
33
by its
HCF 11 in order to bring it into its simplest/lowest form:
22
33
=
22 ÷ 11
33 ÷ 11
=
2
3
Step 5
Hence, the simplest/lowest form of
22
33
is
2
3
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [6]
E)
1 20
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
11
220
in the simplest/lowest form, let us find the HCF of 11 and 220:
11 | 11
| 1
Factors of 11 = 11
2 | 220
2 | 110
5 | 55
11 | 11
| 1
Factors of 220 = 2 × 2 × 5 × 11
The HCF of 11 and 220 is 11.
Step 4
Now, let us divide both the numerator and denominator of the fraction
11
220
by its
HCF 11 in order to bring it into its simplest/lowest form:
11
220
=
11 ÷ 11
220 ÷ 11
=
1
20
Step 5
Hence, the simplest/lowest form of
11
220
1
is
20
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [7]
F)
1 11
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
7
77
in the simplest/lowest form, let us find the HCF of
7 and 77:
7 | 7
| 1
Factors of 7 = 7
7 | 77
11 | 11
| 1
Factors of 77 = 7 × 11
The HCF of 7 and 77 is 7.
Step 4
Now, let us divide both the numerator and denominator of the fraction
7
77
by its
HCF 7 in order to bring it into its simplest/lowest form:
7
77
=
7 ÷ 7
77 ÷ 7
=
1
11
Step 5
Hence, the simplest/lowest form of
7
77
1
is
11
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [8]
G)
1 3
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
9
27
in the simplest/lowest form, let us find the HCF of
9 and 27:
3 | 9
3 | 3
| 1
Factors of 9 = 3 × 3
3 | 27
3 | 9
3 | 3
| 1
Factors of 27 = 3 × 3 × 3
The HCF of 9 and 27 is 3 × 3 = 9 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
9
27
by its
HCF 9 in order to bring it into its simplest/lowest form:
9
27
=
9 ÷ 9
27 ÷ 9
=
1
3
Step 5
Hence, the simplest/lowest form of
9
27
is
1
3
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [9]
H)
15 19
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
120
152
in the simplest/lowest form, let us find the HCF of 120 and 152:
2 | 120
2 | 60
2 | 30
3 | 15
5 | 5
| 1
Factors of 120 = 2 × 2 × 2 × 3 × 5
2 | 152
2 | 76
2 | 38
19 | 19
| 1
Factors of 152 = 2 × 2 × 2 × 19
The HCF of 120 and 152 is 2 × 2 × 2 = 8 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
120
152
by its
HCF 8 in order to bring it into its simplest/lowest form:
120
152
=
120 ÷ 8
152 ÷ 8
=
15
19
Step 5
Hence, the simplest/lowest form of
120
152
is
15
19
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [10]
(C) 2015 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibitated

ID : ae-4-Convert-Mixed-to-Improper-Fraction [11]
J)
9 20
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
36
80
in the simplest/lowest form, let us find the HCF of
36 and 80:
2 | 36
2 | 18
3 | 9
3 | 3
| 1
Factors of 36 = 2 × 2 × 3 × 3
2 | 80
2 | 40
2 | 20
2 | 10
5 | 5
| 1
Factors of 80 = 2 × 2 × 2 × 2 × 5
The HCF of 36 and 80 is 2 × 2 = 4 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
36
80
by its
HCF 4 in order to bring it into its simplest/lowest form:
36
80
=
36 ÷ 4
80 ÷ 4
=
9
20
Step 5
Hence, the simplest/lowest form of
36
80
is
9
20
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [12]
(C) 2015 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibitated

ID : ae-4-Convert-Mixed-to-Improper-Fraction [13]
L)
4 5
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
44
55
in the simplest/lowest form, let us find the HCF of
44 and 55:
2 | 44
2 | 22
11 | 11
| 1
Factors of 44 = 2 × 2 × 11
5 | 55
11 | 11
| 1
Factors of 55 = 5 × 11
The HCF of 44 and 55 is 11.
Step 4
Now, let us divide both the numerator and denominator of the fraction
44
55
by its
HCF 11 in order to bring it into its simplest/lowest form:
44
55
=
44 ÷ 11
55 ÷ 11
=
4
5
Step 5
Hence, the simplest/lowest form of
44
55
is
4
5
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [14]
M)
1 4
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
6
24
in the simplest/lowest form, let us find the HCF of
6 and 24:
2 | 6
3 | 3
| 1
Factors of 6 = 2 × 3
2 | 24
2 | 12
2 | 6
3 | 3
| 1
Factors of 24 = 2 × 2 × 2 × 3
The HCF of 6 and 24 is 2 × 3 = 6 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
6
24
by its
HCF 6 in order to bring it into its simplest/lowest form:
6
24
=
6 ÷ 6
24 ÷ 6
=
1
4
Step 5
Hence, the simplest/lowest form of
6
24
is
1
4
.
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [15]
N)
5 12
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
60
144
in the simplest/lowest form, let us find the HCF of 60 and 144:
2 | 60
2 | 30
3 | 15
5 | 5
| 1
Factors of 60 = 2 × 2 × 3 × 5
2 | 144
2 | 72
2 | 36
2 | 18
3 | 9
3 | 3
| 1
Factors of 144 = 2 × 2 × 2 × 2 × 3 × 3
The HCF of 60 and 144 is 2 × 2 × 3 = 12 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
60
144
by its
HCF 12 in order to bring it into its simplest/lowest form:
60
144
=
60 ÷ 12
144 ÷ 12
=
5
12
Step 5
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Hence, the simplest/lowest form of
60
144
is
5
12
.
ID : ae-4-Convert-Mixed-to-Improper-Fraction [16]
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ID : ae-4-Convert-Mixed-to-Improper-Fraction [17]
O)
1 3
Step 1
A fraction is said to be in the simplest/lowest form if its numerator and the denominator have no common factor higher than 1. In other words, we can say that a fraction is said to be in the simplest/lowest form if the HCF of its numerator and denominator is equal to 1.
Step 2
If for any fraction, both the numerator and the denominator are divided by their
HCF, the HCF of the new numerator and denominator will be 1. This means that the new fraction will be in its simplest/lowest form.
Step 3
In order to write the fraction
12
36
in the simplest/lowest form, let us find the HCF of
12 and 36:
2 | 12
2 | 6
3 | 3
| 1
Factors of 12 = 2 × 2 × 3
2 | 36
2 | 18
3 | 9
3 | 3
| 1
Factors of 36 = 2 × 2 × 3 × 3
The HCF of 12 and 36 is 2 × 2 × 3 = 12 .
Step 4
Now, let us divide both the numerator and denominator of the fraction
12
36
by its
HCF 12 in order to bring it into its simplest/lowest form:
12
36
=
12 ÷ 12
36 ÷ 12
=
1
3
Step 5
Hence, the simplest/lowest form of
12
36
is
1
3
.
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