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!

Quicker Addition: Left to Right Math

Dr. Benjamin Arthur ,of the book The Secrets of Mental Math, encourages kids and adults alike to try adding left to right instead of right to left. The reason is simple. We are taught to read left to right, we write left to right, and are therefore more adept at thinking left to right. Only in math do we reverse the routine.

Here is how left to right addition works. Take an addition problem, such as 34 + 45. Add the tens columns first (34 + 40 = 74). Now add the ones column (74 + 5 = 79).

Try these examples in your head. I will pitch in some three digit numbers as well.

______23                       62                     134

_____+42                    +26                   + 63

This is all  very good, but what if I throw in much bigger numbers, such as…

___256

__+289

Not only are the numbers bigger, but they include carrying-over. Here’s a trick.

Round-up the bottom number to 300. Now add 300 to 256. Then subtract the difference between 300 and 289, which is 11.

Hence, 256 + 289 = 256 + 300 – 11.

Then 256 + 300 = 556

556 -11 = 556 – 10 -1

556-10 = 546 and finally 546 -1 =545 Your answer is 545.

Try these: 645 + 276     and    327 + 499

What we learned:

* Adding left to right can be faster.

* With big numbers it is often quicker to round up the bottom number and subtract the difference from the sum.

On Friday I will share how you can build on left to right math with subtraction!