Page 74 - ICSE Math 6

Like and unlike fractions

Fractions having the same denominator are known as like fractions Maths Info
and fractions with different denominators are known as unlike Unlike fractions can be equivalent
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fractions. For example, , and are like fractions whereas fractions such as 3 and 12 which
25 25 25 are unlike but equivalent.
7 7 and 12 are unlike fractions.
,
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Reducing a Fraction to Its Lowest Terms

A fraction is in its lowest terms or simplest form if its numerator and denominator have no common
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factor except 1. For example, the fractions , , and are in their lowest terms. A fraction is
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always expressed in its lowest terms or simplest form.
A fraction can be reduced to its lowest terms by the following methods.

(a) Prime Factorization Method (b) HCF Method
Prime factorization method
Step 1: Write the numerator and the denominator as the product of their prime factors.

Step 2: Cancel the common factors to get the fraction in the lowest terms.

Example 7: Convert 18 into its lowest terms using the prime factorization method.
48
18 2 × 3 ×3 3
Solution: = =
48 2 ×2×2×2× 3 8
HCF method
Step 1: Find the HCF of the numerator and the denominator.
Step 2: Divide each term of the fraction by the HCF to get the fraction in the lowest terms.
36
Example 8: Convert into its lowest terms using the HCF method.
144
Solution: The HCF of 36 and 144 is 36.

On dividing the numerator and the denominator of the fraction by 36, we get:
36 36 36÷ 1
= =
144 144 36÷ 4
1
Thus, the simplest form of 36 is .
144 4

Conversion of Fractions
Conversion of mixed fraction into improper fraction
b
We can convert any mixed fraction a into an improper fraction by using the given formula:
c
b {Whole part (a) × Denominator (c)} + Numerator (b)
Mixed fraction a = Denominator (c)
c
2
Example 9: Convert 1 into an improper fraction.
3
2 (1×3) +2 3+2 5
Solution: 1 = = =
3 3 3 3

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