Page 30 - Revised Maths Wisdom Class - 6

28 MATHS

Subtraction of Integers
As we know, subtraction is the inverse process of addition. Subtraction of integers can be done easily using this
fact. For example, subtracting 6 from 17 is the same as adding the additive inverse of 6 to 17.

i.e., 17 – 6 = 17 + (–6) = 11
In other words, if a and b are two integers, then a – b = a + (–b)

Similarly, subtracting –7 from 13 is the same as adding the additive inverse of –7 to 13.
⇒ 13 – (–7) = 13 + 7 = 20

i.e., a – (–b) = a + b

Subtraction of Integers on Number Line
Subtracing –6 from 7 is the same as finding an integer which when added to –6 gives 7 i.e., + (–6) = 7

Using number line we can find the answer.
We start from –6 and count the number of steps to reach 7. We see that we move 13 steps to the right to

–6 to reach 7. 13 steps to right or +13

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

Thus, 13 + (–6) = 7.
Now, using the number line let us find the value of:

(i) –4 – (–2) (ii) 7 – (–2)
(i) –4 – (–2) can be written as + (–2) = –4 Or what should be added to –2 to get –4.

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

We see that to reach –4 from –2 we need to move 2 steps to the left of –2.
Therefore (–2) + (–2) = –4
or –2 = –4 – (–2)

(ii) 7 – (–2) can be written as + (–2) = 7 Or what should be added to –2 to get 7.

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
Thus we see that we need to move 9 steps to the right of –2 to reach 7.
Therefore 7 – (–2) = 9.

Properties for Subtraction of Integers
1. Closure Property: For any two integers a and b, their difference a – b is also an integer.
For example, – 6 – (– 3) = – 6 + 3 = – 3 is an integer

2. Commutative Property: For any two integers a and b, a – b ≠ b – a
Thus, subtraction is not commutative for integers.

For example, 6 – 8 = 6 + (– 8) = –2