Mental math tricks for all four operations

A handful of methods covers almost every sum you meet day to day. Each one turns a hard problem into two easy ones.

Addition: work left to right

School teaches adding from the right, carrying as you go. In your head it's faster the other way: add the tens first, then the ones. You hold one number at a time, and the big part of the answer arrives first.

When one number is just under a round number, round it and adjust. Adding 39 is adding 40 and taking one back.

For a three-digit number plus a two-digit one, keep the big number whole and add the small one in two steps.

Subtraction: count up instead

Subtraction is where most people slow down, because borrowing is hard to hold in your head. Turn it around: start at the smaller number and count up to the bigger one, the way a shopkeeper counts out change.

Rounding works here too. Subtracting 39 is subtracting 40 and giving one back.

With bigger numbers, take away the tens, then the ones.

Multiplication: split the bigger number

Anything up to 12 × 12 should be a fact you remember rather than work out; the times tables guide has a way to get there. Past that, split the bigger number into tens and ones, multiply each, and add.

A few shortcuts are worth knowing by heart:

• × 9 is × 10 minus the number once.
• × 12 is × 10 plus × 2.
• × 5 is half of × 10.
• A number just under a ten, like 28 or 29, is easier as the ten minus a little.

Division: ask a times-table question

Don't divide; ask what times the divisor makes the number. 72 ÷ 8 is "8 times what is 72?", and if you know your tables the answer is already there.

For a bigger number, split it into parts the divisor goes into cleanly, usually a round ten-times part and the rest.

Two more shortcuts: dividing by 4 or 8 is halving two or three times, and dividing by 5 is doubling and then dividing by 10.

Dividing by a two-digit number, guess with the round number nearby, then check by multiplying. The answer is a single digit, so you rarely need more than two tries.

Make them automatic

A trick only saves time once you no longer have to think about using it. That takes a little practice every day: a few minutes of problems is enough, as long as you're doing them fast. The guide to getting faster explains how to practise so it sticks.

Questions

What is the fastest way to add in your head?

Add from the left: tens first, then ones. When a number is close to a round one, add the round number and adjust, so 57 + 39 becomes 57 + 40 − 1.

How do you subtract big numbers mentally?

Count up from the smaller number to the bigger one in easy steps, or round the number you are taking away and adjust. 124 − 39 is 124 − 40 + 1.

How do you divide in your head quickly?

Turn it into a times-table question: 72 ÷ 8 asks what times 8 makes 72. For bigger numbers, split the number into parts the divisor goes into cleanly.