Page 118 - Start Up Mathematics_4

3 5
Example 21: Subtract from and reduce the difference Common Mistake!
8 8
2
to the lowest terms. 4 + = 4 + 2 = 6 ()
7 7 7 + 7 14
5 3 5 – 3 2 2 1 5 3 5 – 3 2
Solution: – = = = = – = = ()
8 8 8 8 2 × 2 × 2 4 8 8 8 – 8 0

To add or subtract unlike fractions, convert them to like fractions and then add or subtract
them.
2 5
Example 22: Add and and reduce the sum to its lowest terms.
3 6
2 2 × 6 12 5 5 × 3 15
Solution: = = = =
3 3 × 6 18 6 6 × 3 18
2 5 12 15 12 + 15 27 3 × 3 × 3 3
+ = + = = = =
3 6 18 18 18 18 3 × 3 × 2 2
2 5 3
So, + = .
3 6 2

3 8
Example 23: Subtract from and reduce the difference to its lowest terms.
5 10
3 3 × 10 30 8 8 × 5 40
Solution: = = = =
5 5 × 10 50 10 10 × 5 50
8 3 40 30 40 – 30 10 5 × 2 1
– = – = = = =
10 5 50 50 50 50 5 × 5 × 2 5
8 3 1
So, – = .
10 5 5

To add or subtract mixed fractions, first convert them to improper fractions then to like
fractions and then add or subtract them.
1 3
Example 24: Find the sum and difference of 1 and 2 .
2 4
1 (1 × 2) + 1 3 3 (2 × 4) + 3 11
Solution: 1 = = 2 = =
2 2 2 4 4 4
3 3 × 4 12 11 11 × 2 22
= = = =
2 2 × 4 8 4 4 × 2 8
12 22 12 + 22 34 2 × 17 17
+ = = = =
8 8 8 8 2 × 2 × 2 4
1 3 17
So, 1 + 2 = .
2 4 4
22 12 22 – 12 10 2 × 5 5
– = = = =
8 8 8 8 2 × 2 × 2 4
3 1 5
So, 2 – 1 = .
4 2 4

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