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rEDUCing A FrACtion to itS LowESt tErMS

A fraction is said to be in its lowest term (or simplest form) if the numerator and

denominator have no common factor except 1.

To reduce a fraction to its lowest term, the numerator and denominator of the fraction
are divided by their HCF.

18 27
Example 1. Reduce to its lowest term. Example 2. Find the lowest term of .
30 63

Solution. Numerator = 18, denominator = 30 Solution. Numerator = 27, denominator = 63

18 = 2 × 3 × 3; 30 = 2 × 3 × 5 27 = 3 × 3 × 3 and 63 = 3 × 3 × 7
The HCF of 18 and 30 is 2 × 3 = 6. So, the HCF of 27 and 63 is 3 × 3 = 9.

So, we divide the numerator and 27 27 ÷ 9 3
denominator of the fraction by 6. Now, 63 = 63÷ 9 = .
7
3
18 = 18 ÷ 6 = 3 Therefore, the lowest term of 27 is .
30 30 ÷ 6 5 63 7
3 18
Hence, is the lowest term of .
5 30

CoMPAring AnD orDEring FrACtionS

Comparing Like Fractions Like fractions
Look at the given pairs of fractions and compare them by are fractions

observing the figures. with the same
denominator.
4 3 5 7 7 5
a. and b. and c. and
5 5 8 8 10 10

Clearly,

Thus, if the fractions are like fractions, the fraction with the greater numerator is
greater than the other.

2 8 4 5
Example 1. Arrange the fractions , , , in ascending order.
9 9 9 9

94 Mathematics 5