Adding Three Numbers

You can choose the order

Here is a powerful fact: when you add numbers, you can add them in any order and still reach the same total. So when three numbers wait to be added, you do not have to plod through them left to right. You can be clever and pick the easiest pair first.

This freedom is what makes adding three numbers fun rather than fiddly. The trick is knowing which pair to choose.

Strategy 1: look for a tidy ten

The best pair to add first is one that makes a tidy 10, because adding to 10 is so easy.

Take 7 + 5 + 3. Scan for a pair that makes 10. The 7 and the 3 do it!

• 7 + 3 = 10
• 10 + 5 = 15

So 7 + 5 + 3 = 15. We jumped over the awkward middle and used a friendly 10. To spot these pairs instantly, keep your number bonds to 10 sharp.

Strategy 2: look for a double

If no pair makes 10, look for a double or near double, because those are quick to recall.

Take 9 + 2 + 9. The two 9s make a double:

• 9 + 9 = 18
• 18 + 2 = 20

So 9 + 2 + 9 = 20.

Choosing the smart order

Let's compare the lazy order with the smart order.

Sum	Smart pair first	Then add	Total
7 + 5 + 3	7 + 3 = 10	+ 5	15
4 + 8 + 6	4 + 6 = 10	+ 8	18
6 + 7 + 4	6 + 4 = 10	+ 7	17
9 + 2 + 9	9 + 9 = 18 (double)	+ 2	20
8 + 5 + 2	8 + 2 = 10	+ 5	15

In every row, doing the clever pair first turns a three-number sum into one easy step.

Worked example 1: making ten

Work out 4 + 8 + 6.

1. Hunt for a pair making 10: 4 + 6 = 10.
2. Add the leftover number: 10 + 8 = 18.

So 4 + 8 + 6 = 18.

Worked example 2: no ten, use a double

Work out 5 + 7 + 5.

1. No pair makes exactly 10, but 5 + 5 = 10 does — there are two 5s!
2. 5 + 5 = 10, then 10 + 7 = 17.

So 5 + 7 + 5 = 17. (Two 5s are a double and a ten — even better.)

Worked example 3: checking by reordering

Work out 6 + 7 + 4 the smart way, then check.

Smart way: 6 + 4 = 10, then 10 + 7 = 17.

Check left to right: 6 + 7 = 13, then 13 + 4 = 17. Same answer — proof the order does not matter.

Why this strategy matters

Reordering to add is one of the first times you take control of a calculation instead of following one fixed path. It builds number sense, speeds you up, and reduces mistakes because you work with friendly numbers like 10 and doubles. The same flexible thinking helps later with column addition and longer mental sums.

Try it yourself

You will need a dice (or three) and paper.

1. Roll three dice (or one dice three times) and write the numbers down.
2. Look for a pair that makes 10, or a double, and ring it.
3. Add that pair first, then add the last number.
4. Say your plan aloud: "6 and 4 make 10, plus 7 is 17."
5. Challenge: Check by adding in a different order — do you get the same total?

What's next?

Once you choose smart orders, your mental adding will fly. Practise more shortcuts in mental math strategies, and try the written method in column addition with carrying.