Monday, March 24, 2014

Early in elementary school students are taught how to subtract single digit numbers. Then students progress to subtraction of two digit numbers, which is taught from right to left. For many people, it's easier to add than subtract, but if you use the same left to right method of subtraction like I showed in addition in a previous article, subtraction can be almost as simple as addition.

To subtract two digit numbers mentally from left to right, you want to try to simplify the problem so that you are subtracting or adding a one digit number. Let's start with a simple example, 75 minus 23. The idea is to make each subtraction easier until you get the final answer. Break down the second number to a number in base 10 and another number. So break down 23 to 20 and 3. Now take 75 minus 20 to get 55 and subtract 3 to get the final answer of 52. A problem without borrowing is very simple, whether subtracting from left to right or right to left.

Let's try another example, this time with borrowing. For example, 55 minus 37. In this problem we have to borrow. This occurs when the larger number is being subtracted from the smaller number. There are two different ways to approach such problems. First, you can change 37 to 30 and 7 and subtract 30 from 55 first to get 25 then subtract 7 to get 18. But in this case, it's easier to subtract in a different way. Change 37 to 40 minus 3. By doing this we subtract 40 from 55 to get 15 and add back the 3 to get 18.

The easy way to decide which method to use is to see if you have to borrow or not. If there is borrowing involved, round the number you are subtracting up to the next 10, subtract that and add back the difference. Notice that's what I did in the above example. I subtracted 40 from 55 to get 15 and added back the 3 to get 18. If there is no borrowing involved, round the number down and subtract all the way through.

Let's try another example. Take 47 minus 29. Since there is borrowing involved, change 29 to 30 minus 1. Now subtract 30 from 47 to get 17 and add 1 back to get 18. With a little practice, you'll be able to solve subtraction problems using both methods.

When subtracting a three digit number from another three digit number, you used the same principles. If there is no borrowing involved the subtraction is easily done from left to right. Take 645 minus 124. Change 124 to 100 plus 20 plus 4. Now subtract 100 from 645 to get 545. Subtract 20 from 545 to get 525 and finally subtract 4 to get 521.

Take an example of subtracting three digit numbers with borrowing. Try 423 minus 219. We can either change 219 to 200 plus 10 plus 9 and subtract to get 423 minus 200 equals 223, 223 minus 10 equals 213, and 213 minus 9 equals 204. Or we can change 219 to 300 minus 81. Now we subtract 300 from 423 to get 123 and add back 81 to get 204. The choice on which method you use is entirely up to you. Both will work nicely, it's a matter or personal preference.

These are some techniques I have used over the years as a math tutor to help encourage students to perform more math mentally instead of relying on a calculator. There will be more mental math articles to come. Enjoy!

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