Mental Math Tricks

Multiples of 5

Multiples of 10 are easy to calculate mentally because you can simply add 0 (or a decimal place) to the end of the number that you're multiplying by 10. Next time you're multiplying a number by 5, figure out what half of the number is, then multiply that number by 10.

Take 5 x 14.

Cut 14 in half to get 7.

10 x 7 = 70. (Look at that, 5 x 14 = 70, too!)

This method also works for odd numbers. For example, 5 x 19 is the same as 10 x 9.5, or 95.

Multiples of 11

Instead of multiplying numbers by 11, multiply them by 10 first. Next, add the number itself (which is really the number multiplied by 1) to get the total, like this:

11 x 11 becomes 10 x 11 = 110, plus 11 more, which gives an answer of 121.

It works for larger numbers, too.

11 x 58

10 x 58 = 580

580 + 58 = 638

Distributive Property of Multiplication

Now that you've unlocked the secret to breaking down problems into parts, here's another trick that every 'mathemagician' should know - the distributive property of multiplication.

When we multiply 2- or 3-digit numbers, it can be challenging to keep track of all the numbers in our heads. However, if we break down (or 'decompose') the larger numbers into smaller parts, they become more manageable. Try this technique with larger multiples, such as:

12 x 12.

It's the same as 12 x 10 + 12 x 2 (if we 'distribute' 12 to 10 and to 2).

These smaller pieces can be mentally calculated to get 120 + 24 = 144.

Now, let's try multiplying a 1-digit number by a 3-digit number.

First, decompose 8 x 467 by distributing the 8. Make it easier to figure out in your head by using the nearest multiples of 100 and 10.

8 x 400 + 8 x 60 + 8 x 7

3200 + 480 + 56 = 3736

Saying each of the partial sums out loud may help you remember them as you mentally multiply and add together each part. For our example, you might say, '3200, 3680, 3736' to help remember the totals as you go. The more you practice mental math, the easier it will become.

Divide and Conquer

By now, you're probably convinced that calculating math in your head is painless once you break numbers down into parts. Apply this same method to division. If you want to divide a number by 4, cut it in half (which is dividing by 2) and then cut it in half again. To divide a number by 8, halve it 3 times.

Check out these clever tricks for figuring out which number to divide by (the divisor). If the number that you want to divide (the dividend) is evenly divisible by 5, it ends in a zero or a 5. At a glance, we can tell that 7,847,295 is divisible by 5.

To determine whether a number can be divided evenly by 3, add up all of its digits until you have a single digit. If it's a power of 3 (3, 6, 9), then the dividend can be divided by 3. For example:

3762

3 + 7 + 6 + 2 = 18

1 + 8 = 9

9 is a power of 3, so 3762 can be divided evenly by 3.

If a number is divisible by 3 and ends in a 0 or an even number, then it's also divisible by 6.