Numbers Near 10

To help multiply two numbers near 10 in your head, this article will provide a convenient shortcut. Practice by selecting numbers of your own and work through each category until you're confident you understand the process and are getting the correct answer each time.

Both Numbers Above 10

To start off, we'll work with an equation in which both numbers are above 10. For this section's example, we'll multiply 14 * 13.

First, we subtract 10 from both 14 and 13:

14 - 10 = 4
13 - 10 = 3

Next, you're going to add either number's difference from the opposing number from the equation. In this example, you can either add 4 to 13 or 3 to 14 (you'll get the same answer either way):

4 + 13 = 17
or
3 + 14 = 17

This number is then multiplied by 10 (the reference point we've been using):

17 * 10 = 170

The two differences are then multiplied together:

3 * 4 = 12

Finally, you add this number to the previous answer:

170 + 12 = 182

Thus, the answer to 14 * 13 is 182!

Let's try another example, this time with 12 * 15. We start by subtracting 10 from both numbers:

12 - 10 = 2
15 - 10 = 5

Next, we add either number's difference to the opposing number:

2 + 15 = 17
or
5 + 12 = 17

This number is multiplied by 10:

17 * 10 = 170

The two differences are multiplied (2 * 5 = 10) and then added to the previous answer:

170 + 10 = 180

This gives us 15 * 12 = 180.

Both Numbers Below 10

The process for multiplying two numbers below 10 is the same as above, except that you start dealing with negative numbers. For this example, we'll use 6 * 8.

First, we subtract 10 from both numbers:

6 - 10 = -4
8 - 10 = -2

Next, one numbers difference is added to the other number (notice that the addition of a negative number is effectively a subtraction):

-4 + 8 = +4
or
-2 + 6 = +4

This number is then multiplied by 10:

4 * 10 = 40

Finally, the two differences are multiplied together (-4 * -2 = +8) and added to the previous answer:

40 + 8 = 48

Numbers Above AND Below 10

When you're multiplying two numbers in which one is above 10 and the other is below 10, the process is the same as the above, except that negative numbers play a bigger role. In this section, we'll use 8 * 13 as the example.

We start by subtracting 10 from both sides:

8 - 10 = -2
13 - 10 = 3

Next, add either number's difference to the opposing number:

3 + 8 = 11
or
-2 + 13 = 11

Multiply this number by 10:

11 * 10 = 110

In this next step, it's important to take signs into consideration. As before, we multiply the differences of the two numbers:

-2 * 3 = -6

Finally, we add this answer to the previous answer:

-6 + 110 = 104

This gives us the answer of 8 * 13 as 104.