Page 208 - Ganit Kaushal

 5
8. Asha and Somu have bookshelves of the same size, partly filled with books. Asha’s shelf is   th

6
 2
full and Somu’s shelf is   th full. Whose bookshelf is fuller?

5
3 3
9. Rakesh exercised for of an hour, while Rohit exercised for of an hour. Who exercised for a
longer time? 6 4

7.6 ADDITION AND SUBTRACTION OF FRACTIONS

Addition and Subtraction of like Fractions

To add/subtract like fractions, we use the following two formulae.
Sum of Numerators
Addition of like fractions =
Common Denominaator
Difference of Numerators Remark
Subtraction of like fractions =
Commoon Denominator To add or subtract like fractions,
For examples: simply add the numerators or subtract
the numerators as asked without
1 2 12 3 changing the denominator.
+
(i) + = = = 1 If addition and subtraction both are
3 3 3 3 asked in the same question then add
8 3 83 5 and subtract numerators in the same
−
(ii) − = =
11 11 11 11 order as asked without changing
5 2 4 52 4 ( 5 + 4 − 2 92 7 the denominator as shown here in
−
−+
)
(iii) − + = = = = example (iii).
13 13 13 13 13 13 13
Addition and Subtraction of Unlike Fractions
Adding and subtracting fractions with different denominators (unlike fractions) is done by making them like
fractions. The method of adding and subtracting fractions was explicitly described in general by Brahmagupta,
an Indian mathematician, in the year 628 CE!
The steps to add or subtract unlike fractions in Brahmagupta’s method are as follows:
Step 1. Find equivalent fractions so that the denominator is common to all fractions. This can be done by
finding a common multiple of the denominators (e.g., the product of the denominators or the Least Common
Multiple (LCM) of the denominators).

Step 2. Add or subtract these equivalent fractions with the same denominator. This can be done by adding or
subtracting the numerators and keeping the same denominator.
Step 3. Express the result in the lowest terms if needed.
2 1
Ex 1. Find the sum of and using Brahmagupta’s method. (NCERT)
3 5
Sol. The denominators of the given fractions are 3 and 5. The LCM of 3 and 5 is 15. Then we see that
×
2 = 25 = 10 1 = 13 = 3 .
×
,
×
3 35 15 5 53 15
×
2 1 10 3 13
Therefore, + = + =
3 5 15 15 15
206 Mathematics-6