Page 75 - Revised Maths Wisdom Class - 6

Fractions 73

16 4÷ 4 16 28 1
=
28 4÷ 7 16
4
Hence, the simplest form of 16 is . 12 16 1
28 7 12
4 12 3
Alternative Method:
12
by using prime factorization: ×

16
=
28
2 × 2 × 2 × 2 4
= =
2 × 2 × 7 7
3 Alternative Method
Example 5: Write the equivalent fraction of with numerator 21.
5
3 Let the denominator be x
Solution: Given fraction =
5 3 21
Required numerator = 21 ⇒ 5 = x

We know that 21 ÷ 3 = 7 By cross multiplying we get
3 3 × x = 21 × 5
So, multiplying by 7 (numerator and denominator both)
5 7
×
37× 21 ⇒ x = 21 5 = 35
We get = 3
57× 35 21
Hence, the required fraction is 21 Hence, the required fraction is 35 .
35

60 21
Example 6: Reduce to its lowest terms. Example 7: Reduce . to its lowest terms.
135 35
Solution: Using prime factorization: Solution: Using prime factorization:

60 2 × 2 × 3 × 5 4 21 3 × 7 3
= = = =
135 3 × 3 × 3 × 5 9 35 5 × 7 5
4 3
Hence, the lowest term is Hence, the lowest term is
9 5

2
Example 8: Write the equivalent fraction of with denominator 42.
7
2
Solution: Given fraction =
7
Required denominator = 42

RIDDLE
42 ÷ 7 = 6 RIDDLE
Multiplying numerator and denominator by 6 Half of half and one-third of three

2 × 6 = 12 quarters are equal. Do you agree?
7 6 42
12
Hence, the required fraction is .
42