Subtracting Integers
Before we start with subtraction Integers, let us review the terms of Subtraction.
Minuend: The first number from which the second number must be subtracted is called the minuend.
Subtrahend: The second number that is the number that has to be subtracted is called as the subtrahend.
Difference: The answer of subtraction.
To subtract Integers, all we have to do is to add the minuend and the opposite of the subtrahend. Remember that opposite of 5 is -5 and that -9 is 9!
Step 1: Change the sign of the subtrahend. If the subtrahend is positive, then make it negative and if it is negative change it to positive.
Step 2: Change the subtraction sign to addition
Step 3: Follow the rules of addition of Integers.
Addition of Integers
1. If both the numbers have same sign, then add the absolute values and give the common sign to the sum.
2. If the numbers are of opposite signs, then find the difference of the absolute values and give the sign of the number with greater absolute value.
There can be six possible cases.
Case 1: Both the minuend and subtrahend are positive. Like 9 – (+4)
Case 2: Both the minuend and subtrahend are negative. Like -9 – (-4)
Case 3: Minuend is positive and the subtrahend is negative. Like 9 – (-4)
Case 4: Minuend is negative and the subtrahend is positive. Like -9 – (+4)
Case 5: Minuend is zero. Like 0 – (4) or 0 – (-4)
Case 6: Subtrahend is zero. Like 4 – 0 or -4 – 0
Subtraction of Integers can be performed on a number line or using Models like counters or just by following the rules or steps.
Examples
Example 1: Follow rules of subtraction to solve 15 – (-7)
Solution: Step 1: Change the sign of the second number (subtrahend). The opposite of -7 is +7. So -7 is changed to +7
Step 2: Change the subtraction sign to addition. 15 – (-7) = 15 + 7
Step 3: Follow the rules of addition of Integers.
Since both the numbers are positive, we have to add them up and the answer is also positive.
15 + 7 = 22
