Page 200 - Ganit Kaushal

Converting a Fraction into Its Simplest Form

There are two methods we generally use to convert a fraction into its simplest form.
Method 1: (HCF Division Method)

Step 1: Find the HCF of the numerator and the denominator.
Step 2: Divide both the numerator and denominator by the HCF. The resultant fraction is in its lowest /simplest
form.
For example: (i) To write 10 in its simplest form, we divide the numerator and denominator by their HCF,
15
which is 5. Therefore, 10 ÷ 5 = 2 (Simplest form.)
3
15 5
÷
21
(ii) To express in its simplest form, we divide the numerator and denominator by their HCF,
35
÷
which is 7. Therefore, 21 7 = 3 (Simplest form.)
35 7 5
÷
Method 2: (Step-Wise Division Method)
Step 1: Find a factor (prime or composite) that is common to
both the numerator as well as the denominator. Note
Step 2: Divide the numerator and denominator by this Rules of divisibility given in sec. 5.6 of
common factor to get a new fraction. Chapter 5 help in finding such a factor.

Step 3: If the new fraction obtained in step 2 is in simplest form, then stop.
Step 4: If not, repeat steps-1, 2 and 3 till you obtain a fraction in its simplest form.
36
For example: Suppose we want to express in its lowest terms. First, we notice that both the numerator
60
and denominator are even. So, we divide both by 2, and see that 36 = 18 .
60 30 9
Since both the numerator and denominator are still even, we divide each by 2 again; resulting in . We now
3 15
notice that 9 and 15 have a common factor of 3, so we divide both by 3 to get .
5
36 3
Now, 3 and 5 have no common factor other than 1; so, 60 in its lowest terms is .
5
36
Aliter: We could have noticed that in , HCF (36, 60) = 12. Therefore, dividing both the numerator and
60
36 12 3
√
denominator by 12, we could have = . (HCF division method)
√
60 12 5
| Either method works and gives the same answer! But sometimes it can be easier to go in steps.
Algorithm to Find Equivalent Fractions for Two or More Fractions with the Same Unit

Fraction:

Step 1: Find the least common multiple (LCM) of the denominators of the given fractions.
Step 2: Multiply the numerator and the denominator of each fraction by a suitable number to get the LCM
obtained in step 1 as the denominator of all these fractions.

This way, we get equivalent fractions to each of the given fractions with the same fractional units.

198 Mathematics-6