Page 45 - SM Class 5 Inner.cdr

Before we can add or subtract fractions with different denominators, we must first
find fractions with the same denominator, like this :

1. Find the smallest multiple (LCM) of both numbers.

2. Rewrite the fractions as fractions with the equivalent LCM as the
denominator.

When working with fractions, the LCM is called the least common denominator
(LCD).

Take some examples :

2 3
Example 1 : Add and .
3 7

Solution : The LCM (least common multiple) of the denominators 3 and 7 is 21.

So, we convert the given fractions into equivalent with denominator 21.
3 3, 7

7 1, 7
We have, 1, 1

´
´
2 7 14 3 3 9
= and =
´
3 7 21 7 ´ 3 21
+
2 3 14 9 ( 14 9) 23
Therefore, + = + = =
3 7 21 21 214 21
17 15
Example 2 : Find the difference of and .
24 16

Solution : The LCM (least common multiple) of the denominators

24 and 16 is 48.
2 24,16
So, we convert the given fractions into equivalent with denominator 48.
2 12,8
´
´
17 2 34 15 3 45
= and = 2 6, 4
´
´
24 2 48 16 3 48
2 3, 2
15 17
It is clear now, that > 3 3, 1
16 24
1, 1
15 17 45 34
So - = - = 2 × 2 × 2 × 2 × 3 = 48
16 24 48 48
-
(45 34 ) 11
= =
48 48

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