Page 126 - Start Up Mathematics_6

Step 2: Now move 4 steps further to the left of –3 to reach –7.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Thus, we observe that, –3 – 4 = –7.

Case III: Subtraction of a negative integer from a negative integer say –3 from –5, i.e.,
–5 – (–3)
Step 1: On the number line, let’s move 5 steps to the left from 0 to reach –5.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Step 2: The effect of – (–3) will be in the direction opposite to that of –3.

 We move 3 steps to the right of –5 to reach – 2.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Thus, we observe that (–5) – (–3) = –2.

Subtracting b from a is same as adding –b to a.

• Numbers such as 1 and –1, 2 and –2, ..., on adding give the sum zero. Such numbers are called additive
inverse of each other.
• Subtracting a negative integer from any integer is the same as adding its additive inverse.

Example 18: Find:
(a) 40 – (20) (b) 65 – 70 (c) (–12) – (–19) (d) (–12) – (7)

Solution: (a) 40 – 20 = 20 (b) 65 – 70 = –(70 – 65) = –5
(c) (–12) – (–19) = – 12 + 19 = 19 – 12 = 7

(d) (–12) – (7) = –12 + (–7) = –(12 + 7) = –19
Example 19: Fill in the blanks with >, < or =.

(a) (–31) – (–10) ____ (–31) + (–11) (b) 45 – (–11) ____ 60 + (–4)
Solution: (a) LHS = (–31) – (–10) = –31 + 10 = –(31 – 10) = –21
RHS = (–31) + (–11) = –(31 + 11) = –42

Clearly, (–31) – (–10) > (–31) + (–11)
(b) LHS = 45 – (–11) = 45 + 11 = 56

RHS = 60 + (–4) = 60 – 4 = 56
Clearly, 45 – (–11) = 60 + (–4)

Example 20: Fill in the blanks.
(a) (–7) + _____ = 0 (b) 11 + (–11) = _____ (c) (–3) + _____ = –13

Solution: (a) (–7) + 7 = 0 (b) 11 + (–11) = 0 (c) (–3) + (–10) = –13

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