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9  − 8 9  − 8
(b) −   = + addtiveinverseof  
20  15 20  15
9 8  −  8 8 
= + Additive inverseof  is
20 15     15 
 15


93 84 27 32 59
×
×
= + = + = Since, LCM of 15 and 20 is 60.
20 3 15 4 60 60 60
×
×
9  − 8 93  −×
84
×
Alternate method: −   = −  
20  15 20 3  15 4 
×
×
27  −32  27 −− ( 32 ) 59
= −   = =
60  60  60 60
×
3  − 2  − 7 32  −×  − 7
24
(c) +   −   = +   −   [LCM of 10, 5 and 20 is 20]
×
×
10  5   20  10 2  54   20 
6  − 8  − 7
= +   −  
20  20  20 
6 +− ( 8) −− ( 7) Think and Answer
= 2
20 Rohan walks km from a place P, towards
2
−− − ( ) 7 7 5
= east and then from there 1 km towards
20 7
5 1 west. In which direction and how far is he
= = now from the place P?
20 4
We can use a number line to add or subtract rational numbers like fractions.
5 2
For example: Subtract: –1 −
6 3
Strategy: Use a number line.
2
Step 1: Write with a denominator 6 as LCM of 6 and 3 is 6.
3
2 4 5 2 5 4
So, = \ −1 − =−1 −
3 6 6 3 6 6
5
Step 2: Locate –1 on the number line.
6
4 5
Move units to the left of –1 to subtract.
6 6

3 5
–2 –1
6 6
–3 –2 –1 0 1
5 4 3 1
Thus, −1 − =−2 =−2
6 6 6 2
5 2 1
\ −1 − =−2
6 3 2

65 Rational Numbers