Subtraction Of Integers
Subtraction Of Integers
Subtraction of Integers: To subtract integers like a and b, then to subtract b from a, we change the sign of b and add it to a: a – b = a + (-b)
Example: Subtract 3 from -8
Solution: As we have to subtract 3 from -8, we change the sign of 3 and add it to -8. Thus, we have -8 -3 = (-8) + (-3) = -11 . To add two negative integers, first add the absolute value i.e. 8 + 3 = 11, then place the negative sign as both integers are negative. Final answer = -11
Example: Subtract -10 and -11
Solution : -10 - (-11) . Here, the two minus symbol will become plus. So, we get -10 + 11 = +1
If the signs are different subtract the smaller absolute value from the larger absolute value. The sign will be the sign of the integer that produced the larger absolute value.
Example: Simplify: 14 - (+6)
Solution: 14 - (+6) = 14 - 6 = 8. The answer if positive because sign will be used of larger absolute integer which is 14 and it is positive.
Properties satisfied by subtraction:
Example: Verify closure property under subtraction: Subtract -9 from 8:
Solution: 8 - (-9) : Two negative symbols will become plus. 8 + 9 = +17 which is an integer.
Example: Verify commutative property under subtraction for +5 and +2:
Solution: Let a = +5 and b = +2
RHS = b - a = +2 - (+5) = +2 - 5 = -3
LHS = a - b = +5 - (+2) = +5 -2 = +3
. Hence verified.
Example: Verify Associative Property of integers (+9), (-3) and (+4)
Solution: Let a = +9 , b = -3 and c = +4
LHS = (a - b) - c = (+9 - (-3)) - (+4) = (+9 + 3) - 4 = +12 - 4 = +8
RHS = a - (b - c) = +9 - (-3 - (+4)) = +9 - (-3 - 4) = +9 - (-7) = +9 + 7 = +16
. Hence Verified
Find the difference between the smallest and the largest number of the following: - 68, 32, - 32, 0, - 3 | |||
| Right Option : B | |||
| View Explanation | |||
Sum of two integers is +62. If one of the integer is - 48 then the other is __________________________ | |||
| Right Option : D | |||
| View Explanation | |||
Fill in the box with appropriate integer. (-6)+(-24)-(48)=X | |||
| Right Option : B | |||
| View Explanation | |||
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