# Polite Subtraction

Here is a nifty trick for speeding up subtraction of large numbers, generally three digit numbers or a combination of three-digit and two-digit numbers.

For example, to subtract 64 from 260, many of us would scribble on paper or grab a calculator. If the number was 60, many of us would do the equation in our heads, but that 4 takes a little extra effort.

Try this helpful strategy.   Round 64 up to100, then subtract 100 from 260.

260 – 100 = 160.

Now add the difference between 100 and 64. Let’s see, 100-64 = 36, so 36 is the difference. Then add 160 + 36, which equals 196.

“But that was more difficult than just writing it our or using a computer!” you might say.

Hold on. This is the fun part. What seems difficult becomes quick and easy if we use complements. (Yes, be nice to your math and it will be nice to you.)

Look below at the numbers subtracted from 100 and the answers. See a pattern?

100 100 100 100

-81   -68   -33  -24

19    32     67   76

Each of the numbers in the in the ones columns add up to 10. Each of the numbers in the tens columns add up to 9, always.

Oh, that is not exactly true, but the only exceptions are equations that end in zeros, such as 90 – 10 =80, which most of us can do anyway.

Now that you understand complements, try them out with these problems. Check them against a calculator or on paper. Does the method work?

245      416     759

-78       -29      -82

(Let’s do the first one together. Round 78 up to 100. 245 – 100 = 145. The complement of 78 is 22. 145 + 22 = 167)

You can make this even simpler by adding left to right = 145 + 20 = 165, 165 + 2 = 167.

Try these out, then write your own and try to do them in your head. Before long you will be as fast as your calculator!