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NTSE

7th Foundation NTSE

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Concept Detail

Maths / Integers / Subtraction Of Integers

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**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

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