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Like and Unlike Fractions

Fractions having the same denominators are called like fractions, otherwise they are called unlike
fractions.
11 15 10 11 2 1
For example: , ,and are unlike fractions; , ,and are like fractions.
13 12 5 19 19 19
Equivalent Fractions

Two or more different fractions that have the same value
after simplifying them are called equivalent fractions. Equivalent fractions are obtained
2 4 Note: by multiplying or dividing both the
For example: , are equivalent fractions. numerator and the denominator
5 10
a c by the same non-zero number.
If and are two unlike fractions, then we can
b d a c
check by cross-multiplication whether they are equivalent fractions or not. As b d
a c
If ad = bc, then and are equivalent fractions, otherwise not.
b d
Example 2: Check whether the following are equivalent fractions or not.
5 3 11 8
(a) and (b) and
20 12 39 27
Solution: (a) 5 and 3 (b) 11 and 8

20 12 39 27
By cross-multiplication, 5 3 By cross-multiplication, 11 8
20 12 39 27

5 × 12 = 60 and 20 × 3 = 60 11 × 27 = 297 and 39 × 8 = 312
\ 60 = 60 \ 297 < 312
5 3 Thus, 11 and 8 are not equivalent
Thus, and are equivalent 39 27
20 12
fractions. fractions.

Reducing a Fraction to its Simplest Form
A fraction is said to be in its simplest form (or its lowest form) if its numerator and denominator have
no common factor (except 1). A fraction can be reduced to its simplest form by dividing both the
numerator and the denominator by their common factors (or by the Highest Common Factor HCF).
Example 3: Reduce the following fractions into their simplest form.

132 145
(a) (b)
148 200

Solution: (a) 132 = 2 × 2 × 311 = 33 (b) 145 = 5 × 29 = 29
×
148 2 × 2 × 37 37 200 222××× 5 × 5 40
[Q 4 is the HCF of 132 and 148] [Q 5 is the HCF of 145 and 200]

33 132 29 145
Thus, is the simplest form of . Thus, is the simplest form of .
37 148 40 200

31 Fractions and Decimals