Page 106 - Maths Class 06

1 1 ´2 2
= = (Multiplying numerator and denominator by 2)
2 2 ´2 4
1 1 3´ 3
= = (Multiplying numerator and denominator by 3)
2 2 3´ 6

1 1 4´ 4
Also, = = (Multiplying numerator and denominator by 4)
2 2 4´ 8
1 2 3 4
Thus, = = = , all are equivalent fractions.
2 4 6 8
NOTE
Guess how many equivalent fractions of any
given fraction exist? To find an equivalent fraction, we may
divide both the numerator and the
Simplest Form of a Fraction denominator by the same number.

A fraction is said to be in the simplest form if its numerator and denominator have only 1 as their common
28
factor, e g. ., Fraction in its simplest form will be:
36
28 28 2¸ 14 2¸ 7
= = =
36 36 2¸ 18 2¸ 9

28 7
Lowest form of is .
36 9

The simplest way to write the given fraction in the simplest form is to find the HCF of the numerator and
the denominator and then divide both of them by their HCF.
22
EX AM PLE 3. Find the equiv a lent frac tion of with de nom i na tor 11.
121

SO LU TION : Thus, we must di vide the numerator as well as denominator by 11 to obtain desired
equiv a lent frac tion.

5
EX AM PLE 4. Find an equiv a lent frac tion of with de nom i na tor 28.
7
SO LU TION : The given ques tion im plies
5 ?
=
7 28

So, you have to find the numerator of the fraction. You know that 7 × 4 = 28. This means
by multiplying the denominator (7) of the given fraction by 4, you get the denominator of
5
the required fraction. And, to get the equivalent fraction of , you also need to multiply its
7

numerator (5) by 4
5 5 ´ 4 20
Therefore , = =
7 7 ´ 4 28

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