Number Dojo Level: 6
Subtracting Whole Numbers
When you see a subtraction problem, you will be given a minuend and a subtrahend. What's the difference? The difference is that the minuend comes first :). Also, the difference is the result you come up with when you subtract the subtrahend from the minuend.
The Old Way
Most of us spent the subtraction portion of our childhood looking at numbers that were aligned vertically, with the units digits in a perfect column, and the rest of the digits arranged similarly. Here, the minuend is on top, and the subtrahend is below it:
Unfortunately, those were the good old days. When you see a subtraction problem on a number sense test, it will always be written horizontally, with the minuend in front of the subtrahend:
This will determine where you start your calculation. If you are subtracting a bigger number from a smaller one, you need to start with the bigger number, calculate the difference, and then add a "minus sign" in front to make it negative.
Then, subtract the units digits, regrouping when necessary. (If you haven't noticed, I prefer to call it "regrouping" than "borrowing." I am highly averse to debt.) Move on to the tens digits, then the hundreds, etc. Like many types of problems in mathematics, it seems to be quicker moving from right to left.
Example 1: 2016 - 602
- Notice the number in front is bigger, so start with it.
- 6 - 2 = 4. 1 - 0 = 1. 0 - 6 (STOP and realize you need to regroup). 10 - 6 = 4. 2 (NO--1 because you just regrouped). 1 - (an implied) 0 = 1. The difference is 1414.
- Notice the number in front is smaller, so start with the 2nd number.
- 9 - 7 = 2. 0 - 6 (STOP and realize you need to regroup). 10 - 6 = 4. 3 (NO--2 because you just regrouped). 2 - 8 (STOP and regroup again). 12 - 8 = 4. 5 (NO--4 because you just regrouped). 4 - (an implied) 0 = 4. The difference is 4442.
- Don't forget to add the minus sign to get -4442.
- Start with the (bigger) 2nd number. (Who do we appreciate?)
- 8 - 7 = 1. 6 - 5 = 1.... See a pattern? The difference is 1111, but you almost forgot to make it negative!
- The difference is -1111.