Calculation methods for subtraction

How many cookies have you eaten?! Four. But there are still quite a lot left, it’s alright. Kim and Philip have baked 16 cookies, so now there are 16 minus four cookies left. That’s 12.

If there are larger numbers to subtract, such as 428 minus 325, it will be more difficult to count in your head. To make it easier, you can subtract hundreds from hundreds, tens from tens, ones from ones, etcetera: each place value separately. The method is called decomposing numbers. Here is an example: 428 minus 325 equals 400 minus 300 plus 20 minus 20 plus 8 minus 5. But wait, we’re adding the results in each place value?

Yes, to see how much of 428 is still remaining. Which is 100 plus zero plus three, which equals 103. The answer is 103. Another method is to count upwards from the smaller number to the larger one. In this way we get the difference between the numbers.

Let’s use the same numbers, 428 minus 325. Count upwards from 325 until it becomes 428. Let’s start with the ones. Add five to 325, so that the number becomes an exact ten, 330. Carry over five.

Then add 70 to make the number an exact hundred, 400. Carry over 70. To reach 428, 28 more are needed. Carry over 28. The difference is then five plus 70 plus 28.

Decompose into tens and ones. 70 plus 20 is 90. Five plus eight is 13. Then we add 90 and 13 and that equals 103. We got the same answer as last time.

Good! A third method is to write the ones in a column, tens in a column, and hundreds in a column. And subtract the columns separately. This method is called stacking. Always start counting from the right.

Eight minus five is three. Two minus two is zero. Four minus three is one. The answer is again 103. Here is a final example.

428 minus 375. Eight minus five is three. Two minus seven is minus five. What do we do when it becomes minus? Then we borrow from the next place value to the left.

In this case it’s the four. We make a diagonal dash over the digit that we borrowed from, so we know that it will be reduced by one. This ‘one’ is a position higher in the position system. Each higher position is ten times larger than the one to the right. So if we move a one from the four’s to the two’s place it becomes 10.

We write 10 over the place value that is borrowing. Instead of calculating two minus seven like we just did, we now count 12 minus seven which is five. Now we borrowed from the four so there are only three left. Three minus three is zero. We don’t need to write the zero before 53, because it does not change how large the number is.

So the answer to 428 minus 375 is 53. Now at least it’s very easy to count, because I have eaten all the cookies.