Page 117 - Start Up Mathematics_4

Alternatively,

Step 1: Multiply 20 by 3. (20 × 3 = 60) 15

Product = 60 4 60
– 4
Step 2: Divide 60 by 4. (60 ÷ 4 = 15) 20
3 3
So, of 20 = × 20 = 15. – 20
4 4 0

Lowest Terms of Fractions

A fraction is said to be in its lowest terms when its numerator and denominator have only
1 as the common factor. We can reduce a fraction to its lowest terms by following these
steps. Consider the fraction 9 .
36
Step 1: Find the prime factors of the numerator and denominator and identify the common
factors.
Prime factors of 9 = 3 , 3 Prime factors of 36 = 3 , 3 , 2, 2

Step 2: Multiply the common prime factors. 3 × 3 = 9
Step 3: Divide the numerator and the denominator of the fraction by the product of the
common prime factors to get the fraction in its lowest terms.

9 = 9 ÷ 9 = 1
36 36 ÷ 9 4

Example 19: Reduce 8 into its lowest terms.
24
Solution: Prime factors of 8 = 2 , 2 , 2 Prime factors of 24 = 2 , 2 , 2 , 3

Product of common prime factors = 2 × 2 × 2 = 8
8 8 ÷ 8 1
= =
24 24 ÷ 8 3
8 1
So, 24 in its lowest terms is 3 .
Alternatively,

Write the prime factorization of the denominator and the numerator. Cancel
the common factors and write what is left to get the fraction in its lowest terms.
8 2 × 2 × 2 1
24 = 2 × 2 × 2 × 3 = 3

Addition and Subtraction of Fractions

To add or subtract like fractions, add or subtract the numerators and keep the denominator
as it is.
4 2
Example 20: Add and .
7 7
4 2 4 + 2 6
Solution: + = =
7 7 7 7

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