There are four fundamental operations on integers. These operations include addition, subtraction, multiplication, and division.
ADDITION
Adding integers having the same sign
In adding integers of the same sign, you must add the absolute values of numbers, then keep the same sign.
Illustrative Examples:
1. Add (+3) + (+5)
Solution: Add 3 and 5 then keep the sign. The result would be +8.
2. Add (-6) + (-4).
Solution: Add the |-6| and |-4| then keep the sign. The result is -10.
Adding integers having opposite signs
In adding integers of opposite signs, you must get the difference of their absolute values, then copy the sign of the number of greater absolute value.
Illustrative Examples:
1. Add (-5) + (+8).
Solution: Subtract |-5| and |+8| then copy the sign of number with greater absolute value. The result is +3.
2. Add (+3) + (-7).
Solution: Subtract |+3| and |-7| then copy the sign of number with greater absolute value. The result is -4.
SUBTRACTION
To subtract integers, copy the minuend, change the sign of the subtrahend then change the operation to addition.
Illustrative Examples:
1. Subtract (-5) and (-7).
2. Solution: (-5) - (-7)
(-5) + (+7) Copy -5 then change the sign of -7.
Change the operation to addition.
The result is +2.
3. Subtract (+17) and (-20).
Solution: (+17) - (-20)
(+17) + (+20) Copy 17. Take the inverse of -20, that is, 20.
Change the operation to addition.
The result is +37.
4. Subtract (+8) from (-15).
Solution: (-15) – (+8)
(-15) + (-8) Copy -15. Take the inverse of +8, that is, -8.
Proceed to addition.
The result is -33.
5. Subtract (-11) by (-7).
Solution: (-11) - (-7)
(-11) + (+7) Copy -11. Change the sign of +7. Proceed to addition.
The result is -4.
MULTIPLICATION
Multiplying integers having the same sign
When multiplying integers with the same sign, the result is the product of their absolute values with positive sign.
Illustrative Examples:
1. Multiply (+3) by (+6).
Solution: Multiply (+3) and (+6). The result is +18.
2. Multiply (-7) and (-8).
Solution: Multiply (-7) and (-8). Since both the multiplier and multiplicand have negative signs, it follows that the product has positive sign. The result is +56.
Multiplying integers with different signs
In multiplying integers with the different signs, the result is the product of their absolute values with negative sign.
Illustrative Examples:
1. Multiply (-2) by (+5).
Solution: Get the product of (-2) and (+5). Since, the multiplier and multiplicand have different signs, it follows that the product is negative. The result is -10.
2. Multiply (+9) and (-4).
Solution: Multiply (+9) and (-4). Since, the multiplier and multiplicand have different signs, it follows that the result is negative. The product of (+9) and (-4) is -36.
DIVISION
Dividing integers with the same sign
When dividing integers with the same sign, the quotient is the quotient with positive sign.
Illustrative Examples:
1. Divide (+9) by (+3).
Solution: Get the quotient of (+9) and (+3). The sign of the result is positive since the integers have the same sign. The quotient is +3.
2. Find the quotient of (-18) and (-2).
Solution: Divide (-18) and (-2). The result is +9.
Dividing integers with the different signs
When dividing integers with different signs, the result is the quotient with negative sign.
Illustrative Examples:
1. Divide (-24) by (+3)
Solution: Since the integers have different signs, the quotient is -8.
2. Divide (+32) by (-2).
Solution: Since the integers have different signs, the quotient is -16