Subtracting Integers

Subtracting integers is the second operations on integers, among the four fundamental operations on integers.

Subtraction is the inverse process of addition.

For example, subtracting 6 from 24 is the same as adding the additive inverse of 6 to 24.

Therefore, 24 - 6 = 24 + (additive inverse of 6) = 24 + (- 6) = 18

The rule can be extended to subtraction of a negative integer from a positive or negative integer.

For example, subtracting -7 from 16 is the same as adding the additive inverse of -7 to 16.

Therefore, 16 - (-7) = 16 + (additive inverse of -7) = 16 + (7) = 23

Thus, to subtract an integer 'y' from another integer 'x', the additive inverse of 'y' is added to 'x',

i.e.,      x - y = x + (additive inverse of y) = x + (- y)

and      x - (- y) = x + (additive inverse of -y) = x + (y)

Change the sign of the integer to be subtracted and then add.

(i) Subtract: +3 from +9

(+9) – (+3)

Here the +3 is subtracted from +9

= +9 – 3, [(+ 3) changes to (-3)]

Now add +9 and -3 using the addition of integers rule.

= +6

(ii) Subtract: -7 from +12

(+12) - (-7)

Here the -7 is subtracted from +12

= +12 + 7, [(-7) changes to (+7)]

Now add +12 and +7 using the addition of integers rule.

= +19

(iii) Subtract: +8 from -18

(-18) – (+8)

Here the +8 is subtracted from -18

= -18 - 8, [(+ 8) changes to (-8)]

Now add -18 and -8 using the addition of integers rule.

= -26

(iv) Subtract: -4 from -11

(-11) – (-4)

Here the -4 is subtracted from -11

= -11 + 4, [(-4) changes to (+4)]

Now add -11 and +4 using the addition of integers rule.

= -7

(v) Subtract: +44 from +99

(+99) – (+44)

Here the +44 is subtracted from +99

= +99 – 44, [(+ 44) changes to (-44)]

Now add +99 and -44 using the addition of integers rule.

= +55

(vi) Subtract: -63 from +87

(+87) - (-63)

Here the -63 is subtracted from +87

= +87 + 63, [(-63) changes to (+63)]

Now add +87 and +63 using the addition of integers rule.

= +150

(vii) Subtract: +41 from -76

(-76) – (+41)

Here the +41 is subtracted from -76

= -76 - 41, [(+ 41) changes to (-41)]

Now add -76 and -41 using the addition of integers rule.

= -117

(viii) Subtract: -16 from -46

(-46) – (-16)

Here the -16 is subtracted from -46

= -46 + 16, [(-16) changes to (+16)]

Now add -46 and +16 using the addition of integers rule.

= -30

Solved Examples Subtraction of Integers:

1. Find the value of -5 - (-13) using a number line.

Solution:

 -5 - (-13) = -5 + (additive inverse of -13) = - 5 + (13)

On the number line, starting from -5 move 13 units to the right to reach point P, which represents 8.

Thus, -5 - (-13) = 8

2. Subtract the following.

(i) 23 from 9

(ii) -6 from 4

(iii) 4 from -8

Solution:

(i) 9 - 23 = 9 + (additive inverse of 23) = 9 + (- 23) = -14

(ii) 4 - (-6) = 4 + (additive inverse of -6) = 4 + 6 = 10

(iii) -8 - 4 = (-8) + (additive inverse of 4) = (-8) + (-4) = -12

3. Subtract the following.

Solution:

(i) 936 from -53

(ii) -386 from 121

(iii) -2150 from -897

(iv) -2645 from +5189

Solution:

(i) -53 - 936 = -53 + (additive inverse of 936) = - 53 + (-936) = - 989

(ii) 121 - (-386) = 121 + (additive inverse of -386) = 121 + 386 = 507

(iii) -897 - (-2150) = -897 + (additive inverse of -2150) = -897 + 2150 = 1253

(iv) 5189 - (-2645) = 5189+ (additive inverse of-2645) = 5189 + 2645 = 7834

4. Subtract the sum of 225 and -299 from the sum of -342 and 151

Solution:

225 + (- 299) = - (299 - 225) = - 74

- 342 + 151 = - (342 - 151) = - 191

Required difference (-191) - (-74) = (-191) + (additive inverse of -74)

                                                  = (-191) + 74

                                                  = -117

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