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Reducing Fractions to Lowest Form
Solutions for fraction problems should be shown in their lowest form or smallest
equivalent fraction.
Reducing Fractions Using Division
Find a number that can be divided into both the numerator and denominator. Divide,
then repeat until the numerator and denominator cannot be divided further.
Example
36 ÷ 2 = 18 ÷ 3 = 6 ÷ 2 3
48 ÷ 2 = 24 ÷ 3 = 8 ÷ 2 4
3 is the lowest form of 36
48
4
24 ÷ 3 = 8 ÷ 2 = 4
30 ÷ 3 = 10 ÷ 2 = 5
Reducing Fractions Using Greatest Common Factors
Identify factors and the greatest common factor (GCF) of the numbers.
Example
To reduce 21 to its lowest form, identify the factors of 21 and
28
28.
The set of factors for 21: 1, 3, 7, 21.
The set of factors for 28: 1, 2, 4, 7, 14, 28.
The GCF of 21 and 28 is 7.
Divide
21 ÷ 7 = 3
28 ÷ 7 = 4
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
3 is the lowest form of 21
28
4
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Reducing Fractions to Lowest Form
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Reducing Improper Fractions to Lowest Form
To reduce an improper fraction to its lowest form, divide the denominator into the
numerator. When you reduce an improper fraction to its lowest form, you get a mixed
number.
Examples
A)
9
7
B)
7
1
9
3
8 24
= 1 72
−7
C) 17
5
24
8
= 3
2
3
5 17
− 15
= 3 52
2
D) 7 + 1 = 8 = 1
8 8 8
E) 3 + 2 = 5
4 4 4
F) 4 2 + 1 2 = 5 4 ,
3
3
3
8 represents 1 whole
8
5 represents 1 whole and
4
4 represents 1 whole and
3
1 = → 11
4
4
1 → 11
3
3
Reducing Mixed Improper Numbers to Lowest Form
Examples
A)
B)
C)
61
2
+ 11
2
72
2
24
5
3
+
5
37
5
78
9
7
+1
9
8 15
9
2 represents 1 whole
2
Add 7 + 1 = 8
7 represents 1 whole and the fraction 2
5
5
Add 3 + 1 + 2 = 4 2
5
5
15 represents 1 whole and the fraction 6
9
9
6
Add 8 + 1 +
9
Reduce to lowest form = 9 2
3
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
Numbers: Fractions:
Reducing Fractions to Lowest Form
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Practice: Reducing Fractions
1. Use fraction circles, drawings, a computer or other methods to identify one
equivalent fraction for each of the following:
1, 2 , 5 , 3 , 6, 4, 9 , 2
4 12 10 12 8 6 12 4
Identify the lowest forms of the fractions above.
2. Use reducing strategies, such as identifying GCF, to convert the following
fractions to their lowest terms. The first one has been done for you.
Fraction
Divided by
Lowest form
14
18
20
24
18
27
10
25
12
18
16
36
14 ÷ 2
18 ÷ 2
7
9
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
Numbers: Fractions:
Reducing Fractions to Lowest Form
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3. Use GCF, LCM or other strategies to fill in the missing sections in the table below.
The first one has been done for you.
Fraction
Lowest form
12
16
3
4
5
6
3
4
18
24
1
4
20
55
2
3
28
42
Knowledge and Employability Studio
Mathematics
©Alberta Education, Alberta, Canada (www.LearnAlberta.ca)
Numbers: Fractions:
Reducing Fractions to Lowest Form
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