Simplifying fractions
A fraction is a part of a whole. It has a numerator and a denominator.
For example: 12 here 1 is the numerator and 2 is the denominator. It is represented by the figure given below:
Here, the shape is divided into 2 equal parts, therefore the denominator is 2 and 1 out of 2 parts is shaded, therefore the numerator is 1.
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Simplest form of a fraction
A fraction is said to be in its simplest form if 1 is the only common factor of its numerator and denominator. For example,89,because 1 is the only common factor of 8 and 9 in this fraction.
We simplify fractions because it is always to work or calculate when the fractions are in the simplest form.
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Simplifying proper and improper fractions
Steps:
Find the highest common factor (HCF) of the numerator and denominator.
Divide both the numerator and denominator by HCF.
Example 1: Check if the fraction 715 is in its simplest form?
Solution: Factors of numerator 7 = 1, 7
Factors of denominator 15 = 1, 3, 5, 15
We can see that 1 is the only common factor of 7 and 15
Therefore, 715 in its simplest form.
Example 2: Reduce 1218 in its simplest form.
Solution: Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 18 = 1, 2, 3, 6, 9, 18
Highest common factor (HCF) of 12 and 18 = 6
Dividing the numerator and the denominator by 6 (HCF), we get
12÷6 18÷6 = 2 3
Hence, 23 is the simplest form of the fraction 1218.
Simplifying a mixed fraction
Steps:
 Find the highest common factor (HCF) of numerator and denominator of the fraction.
 Divide both the numerator and the denominator by HCF to get the simplified fraction.
 Write the whole and the simplified fraction together.
Example 4: Matthew has31216of ice cream. How much ice cream does he have in its simplest form?
Solution: Factors of 3 12 16 = 1 4 12 = 1, 2, 3, 4, 6, 12
Factors of 16 = 1, 2, 4, 8, 16
Highest common factor (HCF) of 12 and 16 = 4
Dividing the numerator and denominator by 4 (HCF), we get
12÷4 16÷4 = 3 4
Hence, Matthew has 31216of ice cream with him in its simplest form.
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