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36 40 48 75
Q 36 < 40 < 48 < 75 ⇒ < < <
120 120 120 120
The ascending order of the fractional parts of the track covered by Varun, Dinesh, Maya and Sonam
3 1 2 5
in 10 minutes is: < < < .
10 3 5 8

Clearly, Dinesh covers the maximum part of the track in 10 minutes than others.
Addition and Subtraction of Fractions

Addition and Subtraction of Like Fractions

When two or more like fractions are added or subtracted, we add or subtract the numerators and
write the sum or the difference over the common denominator.

3 5 3 13  5 13 3 2 13 2  3 13
For example: (a) + 1 = + Q 1 = (b) 2 − = − Q 2 =

8 8 8 8  8 8  5 5 5 5  5 5  


313
−
+ 16 13 2 11 1
= = = 2 = = = 2
8 8 5 5 5
Addition and Subtraction of Unlike Fractions
To add or subtract unlike fractions, first we convert them into like fractions. Then, we add or
subtract them as like fractions.
Example 4: Solve the following.

1 3 2 1 3 3 5
(a) 2 + (b) 3 − 2 (c) 2 + 1 −
3 4 7 9 4 5 6
1 3 7 3 2 1 23 19
Solution: (a) 2 + = + (b) 3 − 2 = −
3 4 3 4 7 9 7 9
LCM of 3 and 4 is 12. LCM of 9 and 7 is 63.

Therefore, Therefore,

7 + 3 = 74 + 33 23 19 23 9 19 7
×
×
×
×
×
3 4 34 43 7 − 9 = 79 − 97
×
×
×
28 9 28 9 207 133 207 133
+
−
= + = = − =
12 12 12 63 63 63
37 1 74 11
= = 3 = = 1
12 12 63 63
3 3 5 11 8 5
(c) 2 + 1 − = + −
4 5 6 4 5 6
LCM of 4, 5, and 6 is 60.
Therefore,
−
+
×
×
×
11 + 8 − 5 = 11 15 + 812 − 510 = 165 + 96 − 50 = 165 96 50
×
×
×
4 5 6 415 512 610 60 60 60 60
211 31
= = 3
60 60
33 Fractions and Decimals