# GMAT Math Pro speed tip: Multiplying by 11 or 15

To multiply a two-digit number, *n*, by 11 quickly, do the following: Add the digits of *n*Â and insert this sum between the digits of *n*. For example, 11*36=396. Calculate 3+6=9 and insert 9 between the 3 and 6 of 36 to get 396. If the sum of the digits is a two-digit number, add one to the ten’s digit of *n*, and insert the unit’s digit between the new two-digit number. For example, 11*87=957. Calculate 8+7=15. This is a two-digit number, so add one to the ten’s digit of 87 to get 97. Now, insert the unit’s digit, 5, between the 9 and 7 to get 957. Try this trick a few times and verify your answers with a calculator.

Multiplying any number by 15 can be made easier by thinking of 15 in different forms. For example, 15 is the same as 1.5*10. If we want to multiply 28*15, this is the same as multiplying 28*1.5*10. But why would we want to do this? The trick is realizing that 28*1.5 is the same as increasing 28 by 50%. In other words, all you have to do is take half of 28, 14, and add it to 28 to get 42. Then multiply 42 by 10 to get the answer, 420. So, this method works well with even numbers because it is easy to see what half of an even number is. With odd numbers it is slightly more difficult but still very doable. Let’s say we want to calculate 13*15. You could do it the same way: 13*15=13*1.5*10=19.5*10=195. Or, you could think of 15 as being the same as 3/2 times 10. Now 13*15=13*(3/2)*10. Now you could multiply 3*13 to get 39, and divide 39 by 2 to get 19.5 and then multiply by 10 to get 195. Use whichever method makes you more comfortable.

Despite the fact that 11 and 15 are only 2 out of infinitely many numbers, these tricks are applicable fairly often on the GMAT. Any new method takes some getting used to, so try a few practice problems until you are convinced that these tricks work. If you’re too paranoid to try new things like this on an actual GMAT, you can at least use them as a way to check answers you get from more traditional multiplication methods.

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