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By Benjamin A., Shermer M.
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Extra info for Secrets of mental math
Example text
Next, multiply 2 ؋ 7 ؍14. Then add 280 plus 14 (left to right, of course) to arrive at 294, the correct answer. We illustrate this procedure below. 42 (40 ؉ 2) ؋ 7 ᎏᎏ 40 ؋ 7 ؍280 14 2؋7؍؉ ᎏᎏ 294 We have omitted diagramming the mental addition of 280 ؉ 14, since you learned how to do that computation in the last chapter. At first you will need to look down at the problem while doing the calculation. With practice you will be able to forgo this step and compute the whole thing in your mind.
853 ؊ 692 ؍ ؊ 700 153 ؉ 8 ؍ ؉8 161 Now, I admit we have been making life easier for you by subtracting numbers that were close to a multiple of 100. qxd 5/4/06 1:46 PM Page 25 A Little Give and Take: Mental Addition and Subtraction If you subtract one digit at a time, simplifying as you go, your sequence will look like this: 725 ؊ 468 ؍ 325 ؊ 68 (first subtract 400) ؍ 265 ؊ 8 (then subtract 60) ؍ 257 (then subtract 8) What happens if you round up to 500? 725 ؊ 468 ؍ 225 ؉ ?? (first subtract 500) ؍ ??
For the one on the left, multiply 30 ؋ 9 plus 8 ؋ 9, giving you 270 ؉ 72. The addition problem is slightly harder because it involves carrying a number. Here 270 ؉ 70 ؉ 2 ؍340 ؉ 2 ؍342. qxd 5/4/06 1:45 PM Page 34 34 Secrets of Mental Math problems like these in your head, and those that require you to carry numbers will be almost as easy as those that don’t. Rounding Up You saw in the last chapter how useful rounding up can be when it comes to subtraction. The same goes for multiplication, especially when you are multiplying numbers that end in eight or nine.