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
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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