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!