Tens Complement (What Makes 10)

The tens complement is the number we add to make 10:

Example: The tens complement of 3 is 7, because 3 + 7 = 10

Here are all the tens complements:

Number Tens Complement Why? Because:
0 10 0 + 10 = 10
1 9 1 + 9 = 10
2 8 2 + 8 = 10
3 7 3 + 7 = 10
4 6 4 + 6 = 10
5 5 5 + 5 = 10
6 4 6 + 4 = 10
7 3 7 + 3 = 10
8 2 8 + 2 = 10
9 1 9 + 1 = 10
10 0 10 + 0 = 10

But you only have to remember half the table!

1 + 9 = 10 and 9 + 1 = 10

1 and 9 are partners!

So are 2 and 8, 3 and 7, 4 and 6 and 5 and 5

Ten Frame

Here we see some of these number partners at work:

Ten Frame Numbered
5 and 5 make 10
A Ten Frame with 6 green dots filling the first 6 squares. Four squares are orange, showing that 6 and 4 make 10.
6 and 4 make 10
A Ten Frame with 8 blue dots filling the first 8 squares. Two squares are orange, showing that 8 and 2 make 10.
8 and 2 make 10

Why is this Important?

Knowing the tens complements makes some mental arithmetic easier.

Example: 8 + 5

We can use the tens complement to "bridge" through 10:

  • We know the tens complement of 8 is 2
  • So, we split 5 into 2 + 3
  • 8 + 2 makes 10
  • 10 + 3 = 13

Example: 35 + 8

Start with:
35 + 8
8 and 2 make 10, so:
35 + 10 − 2
Add the 35 and 10:
45 − 2
Subtract the 2:
43

In practice we think quickly like this:

"the tens complement of 8 is 2": 35+10 is 45, −2 is 43

Example: 74 − 9

"9 and 1 make 10": 74−10 is 64, +1 is 65

It is also used in Quick Subtraction.

Practice!

You can practice by using What Makes 10?

Also called 'Number Bonds to 10' or 'Friends of 10', instead of 'Tens Complement'
What Makes 10? Numbers Index