Math Shortcuts That Can Help at Any Age
As foreign as it sounds to some, it’s much easier to subtract when going from left to right rather than from right to left, going through the whole “borrowing” process of regular math procedures. Practice by writing a number down on paper. Make it a four-place number such as 1452. Subtract from that the number 967. Forget everything you’ve learned about borrowing from the “1”, and so forth. Instead, start from the left, and think “14 minus 9”. Before writing down the number, “5”, think “do I need to borrow for the next set?”. Since the next set will be “5 minus 6”, you know you will need to borrow. Instead of writing down the “5”, then, write “4”. Now you have “15 minus 6”, which is “9”. Before writing down the “9” look at the next set of numbers. “Two minus seven”, the next set of numbers, means you’ll have to borrow. Since that’s the case, write down “8” rather than “9”. Now you have borrowed and the last set becomes “12 minus 7” which is “5”, so write it down.
At first the practice will seem strange but, after trying it several times, you’ll discover that this way of borrowing and subtracting becomes much easier. Use sets of figures that have large numbers on the bottom, and smaller ones on top, so that you’ll get plenty of practice with borrowing and subtracting from left to right.
To add numbers quickly, without paper, break them down into sets as well. For example, 462 plus 358 is done in sets of smaller numbers. Start from the left and think: 4 plus 3 is 7. Now you have “7” in your mind as the first number. 6 plus 5 is 11 so you think “1” for the second number and raise the first number by “1”. So now you have 81. Then 2 plus 8 is 10 so think “0” for the third number. And raise the second number to “2”. Now you have 820. The trick is to repeat the numbers as you add to them, like so: Four plus three is seven. Six plus five makes eight-one. Two plus eight makes eight-two-zero. Practice doing this and you’ll get very fast at it.
A way to add smaller numbers quickly is to do so by “5’s” or “10’s”. For instance, to add the numbers 7,8,9,9,6,8,8,5,1,9 and 3, do so in the following manner: 7 plus 8 is 15, plus 10 is 25, minus 1 is 24, plus 10 is 34 minus 1 is 33, plus 6 is 39, plus 10 is 49, minus 2 is 47. Plus 10 is 57, minus 2 is 55, plus 5 is 60, plus 1 is 61, plus 10 is 71, minus 1 is 70, plus 3 is 73. Although this may seem more complicated, when doing it for the first time, it will become second nature to you after you practice awhile. Start with small numbers and you’ll eventually be able to do the same with “hundreds” and even “thousands”. The key is to practice over and over; that’s the only way to get out of the old way of math and get used to the new way.
To add more than two large numbers together, try the following procedure: if you’ve started with, say, the number 364 and you need to add to it the numbers 172 and 250, start with just the 364 and 172. Think like this: 364 plus 100 is 464. Plus seventy is 534. (If it’s easier, do: plus ten, plus ten, plus ten, plus ten, plus ten, plus ten, plus ten). Plus two is 536. Now add the last number, 250, like so: 536 plus 200 is 736, plus 50 is 786 plus zero is 786.
Multiplying some large numbers is very simple too. 300 x 500 can be done easily like so: 3×5 is 15. Now add on all the zeroes you see: 150,000. Numbers that end in zero can all be done in this manner, whether it’s 10 x 100,000 or 50,000 x 200,000. Simply multiply the numbers other than zero, and write that number down. Then add on all the zeroes you see to the end of that number.
Get help with new techniques in math by searching for “mental math” books and articles online or at the library. Get in lots of practice with the new math procedures and, even though it’s slow at first, you’ll soon be adding, subtracting and multiplying like a pro in no time.
