Nowadays calculators are so prevalent that most students wouldn’t know what to do if they didn’t have one to help them work out their calculations. However, they might find themselves in a situation where they don’t have access to a calculator or aren’t allowed to use one, and in these cases, knowing some math “tricks” can come in very handy.

TIP #1

When multiplying or dividing with numbers ending in zeros, drop the zeros and do the multiplication/division problem, then add the zeros back.

Examples:

400 x 200 = 4 x 2 = 8 (and add back the 4 zeros) = 8000

400/20 = 4/2 = 2 (and add back one zero) = 20

TIP #2

Any number whose digits add up to a number that is divisible by three is also divisible by three.

Example:

123 – the sum of 1 + 2 + 3 is 6, which is divisible by 3, so 123 is divisible by 3 (it is equivalent to 41).

TIP #3

When you multiply decimals, initially ignore the decimals and then add them back to your solution.

Example

1.2 x 3

First drop the decimal and think “12 x 3”, which is 36.

Reinsert the decimal place one spot from the right to obtain 3.6

TIP #4

When multiplying numbers whose tens digits are the same and the ones digits add up to ten, multiply the tens digit by the next whole number, multiply the ones digits together and combine the two products.

Example:

61 x 69

First, multiply the tens digit (6) by the next whole number (7). You get 42.

Second, multiply the ones digits together (1 x 9). You get 09 (a leading zero is added for single-digit products).

Third, combine these products together to get the answer of 4209.

TIP #5

When multiplying a 2-digit number by 11, add the digits of the number together and then insert the sum between the two digits to obtain the answer.

Example:

12 x 11

1 + 2 = 3

Insert the 3 between the 1 and the 2 to get the answer of 132.

TIP #6

When finding the fourth power of a number, think of it as being the square of a square.

Example:

3 raised to the fourth power

This is the same as the square of three squared. Three squared is nine and nine squared is 81.

TIP #7

When squaring any number ending in five, multiply the tens digit by the next whole number and then add on 25.

Example:

35 squared

First, multiply the tens digit (3) by the next whole number (4). You get 12.

Second, add on a 25 to get the answer of 1225.

TIP #8

When multiplying numbers whose difference is two, square the number between the two and then subtract 1.

Example:

79 x 81

First, square the number between the two. 80 squared is 6400.

Second, subtract one from this answer to get the solution of 6399.

There are many other marvelous math tricks out there that can help you out in a pinch and also help curb your dependency on the calculator. You may find that for basic or even intermediate work you don’t even need it anymore. Your habit might be curtailed!