Adding by Rounding and Adjusting

A trick for numbers near a ten

Some numbers are awkward to add because they sit just below a tidy ten — numbers like 18, 19, 28 and 29. The round-and-adjust strategy turns them into something friendly: round them up to the nearest ten, add that easy number, then adjust back the small amount you added on.

This method is sometimes called compensation, because you make up for the rounding at the end.

How round and adjust works

Take 47 + 19. The 19 is just 1 below 20, so:

1. Round up: treat 19 as 20.
2. Add the tidy ten: 47 + 20 = 67.
3. Adjust back: you added 1 too many, so take 1 away. 67 − 1 = 66.

So 47 + 19 = 66.

Why take 1 away at the end? Because rounding 19 up to 20 made you add one extra. To keep the answer exact, you must give that extra 1 back. This is the key difference from estimating — estimating leaves you close, but adjusting lands you spot on.

If you would like to practise the rounding part on its own, see our lesson on rounding numbers.

The two-step plan in a table

Sum	Round up to	Easy add	Adjust back	Total
47 + 19	20 (+1)	47 + 20 = 67	− 1	66
56 + 29	30 (+1)	56 + 30 = 86	− 1	85
64 + 18	20 (+2)	64 + 20 = 84	− 2	82
35 + 28	30 (+2)	35 + 30 = 65	− 2	63

The number in brackets is how much you rounded, and that is exactly how much you take back.

Worked example 1: rounding by 1

Work out 56 + 29.

1. Round 29 up to 30 (that is 1 more).
2. 56 + 30 = 86.
3. Take back the 1: 86 − 1 = 85.

So 56 + 29 = 85.

Worked example 2: rounding by 2

Work out 64 + 18.

1. Round 18 up to 20 (that is 2 more).
2. 64 + 20 = 84.
3. Take back the 2: 84 − 2 = 82.

So 64 + 18 = 82. Whatever you round, you take back the same.

Worked example 3: a real-life shop

A game costs £28 and a book costs £15. What is the total?

1. Round £28 up to £30 (2 more).
2. 30 + 15 = £45.
3. Take back the £2: 45 − 2 = £43.

So the total is £43. Shoppers use this trick all the time to add prices quickly.

Why this strategy matters

Round and adjust replaces fiddly carrying with one easy addition and one tiny correction. It works because adding tidy tens is something our brains find simple. Just as importantly, it teaches the idea that you can change a calculation to make it easier, as long as you undo the change at the end — a way of thinking that powers a lot of clever maths.

Try it yourself

You will need a pencil, paper and a list of two-digit numbers ending in 8 or 9.

1. Write a sum like 45 + 19.
2. Round the 8-or-9 number up to the nearest ten and note how much you rounded.
3. Do the easy addition.
4. Take back exactly what you rounded.
5. Challenge: Check your answer with column addition — does it match?

What's next?

Adjusting is a powerful mental tool. Combine it with other shortcuts in mental math strategies, and compare it with the written method in column addition with carrying.