Page 75 - Start Up Mathematics_5

Alternate Method

3
2
4 + 3 = 4 + 3 + 3 + 2
5 7 5 7
= 4 + 3 + 3 + 2
5 7

add the whole add the
numbers fractions

4 + 3 = 7 3 + 2 = 21 + 10 = 21 + 10 = 31
5 7 35 35 35 35
3
2
So, 4 + 3 = 7 + 31 = 7 31 .
5 7 35 35
2
7
Example 19: Subtract 2 from 3 .
9
5
2
Solution: 3 – 2 7
5 9
2
3 = (3 × 5) + 2 = 15 + 2 = 17
5 5 5 5
7
2 = (2 × 9) + 7 = 18 + 7 = 25
9 9 9 9
7
2
3 – 2 = 17 – 25
5 9 5 9 5 5 , 9
LCM of 5 and 9 = 45 3 1 , 9

17 = 17 × 9 = 153 3 1 , 3
5 5 × 9 45 1 , 1

25 = 25 × 5 = 125
9 9 × 5 45
7
2
So, 3 – 2 = 153 – 125 = 153 – 125 = 28 .
5 9 45 45 45 45
Properties of addition of fractions

Commutative Property: Two (or more) fractions can be added in any order.

Example 20: Show that 3 + 2 = 2 + 3 .
4 5 5 4

Solution: Consider 3 + 2
4 5
LCM of 4 and 5 = 20

3 = 3 × 5 = 15 2 = 2 × 4 = 8
4 4 × 5 20 5 5 × 4 20

So, 3 + 2 = 15 + 8 = 15 + 8 = 23 .
4 5 20 20 20 20

Now, 2 + 3 = 8 + 15 = 8 + 15 = 23
5 4 20 20 20 20
So, 3 + 2 = 2 + 3 .
4 5 5 4

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