# Sum to Ten

The Ten Point Circle illustrates the pairs of numbers whose sum is 10.

Taking a further step, if you can notice, there are eight unique groups of three numbers that sum to 10.

1 + 2 + 7 = 10 is an example.

Below are the eight unique groups. What is the significance of this? Why should we remember this?

When several numbers are added, then it becomes useful if we are able to get whole multiples of 10, i.e. 10, 20, 30, 40 and on on.

For example,

2 + 8 + 3 + 4 +3 + 2 + 5 + 3 = ?

In above sum,

• pair 2,8 adds to 10;
• group of 3, 4, 3 adds to 10;
• group of 2, 5, 3 adds to 10;

So, above sum becomes 10 + 10 + 10 = 30.

This can be extended to addition of larger numbers.

For example: 48 + 16 + 61 + 32 + 59 = ? The above sum becomes simple with this method:

Right figure becomes: 10 + 10 + 6 = (2)6

Left figure becoes: 10 + 4 + 5 + 2(carry) = 21

So, above sum = 216

Let’s practice few more sums:

a 73 + 27       b 28 + 23 + 67 + 42           c 31 + 33 + 57 + 69 + 54 + 16           d 49 + 31 + 69 + 21
e 55 + 65       f 18 + 72 + 33                    g 38 + 33 + 42 + 28 + 22                    h 65 + 65