What is a digital root?

A digital root is the single digit you end up with when you add a number’s digits, then add the digits of that total, until one digit is left. For 5274, 5 + 2 + 7 + 4 = 18 and 1 + 8 = 9, so its digital root is 9. It also equals the remainder after dividing by 9, with one twist: when 9 divides a number exactly, its root is 9, not 0.

How do you multiply by 25 in your head?

Multiply by 100 first, then divide by 4, because 25 is a quarter of 100. For 48 × 25, that gives 4800, and a quarter of 4800 is 1200. Dividing by 4 is easiest as halving twice: 4800, then 2400, then 1200. The same idea handles × 50, which is × 100 followed by a single halving.

Which fast multiplication tricks should you learn first?

Start with the tricks that swap one hard step for an easy one: × 5 as × 10 then halve, and the multiply by 11 trick for two-digit numbers. Then move on to squares ending in 5, and to pairs around a round number, such as 48 × 52 = 2500 − 4 = 2496. Each trick fits in one sentence, which makes it easy to keep.

Why does my child struggle with mental math?

Many children struggle because they try to run the written method in their head and lose track of the carried digits. Mental arithmetic tricks replace that with steps that are easy to hold, such as × 10 and then halve. Before your child calculates, ask them to name the pattern first: a 5 at the end, an 11, or two numbers either side of a round one.

Can I use this mental math game in class, and is it free?

Yes to both: all five trick levels run free in a web browser, with no install and no login. In class, write 15², 25², 35² and 45² on the board with their answers, 225, 625, 1225 and 2025, and ask pupils to find the pattern. Then let them predict 55² before anyone multiplies. For whole classes, the schools plan is priced per pupil and gives the teacher one dashboard to see who is getting better.

Math practice · reimagined

Mental Math Shortcuts

This mental math trick game has five Olympic levels, one shortcut each, from 56 × 11 and 115² to the digital root of a six-digit number. Use the trick to answer before your rival, and your fighter lands a blow that grows with your speed.

Ages 4–99+ · no download · plays in your browser · 23 languages

Choose your level ▸

What is a mental math shortcut?

A mental math shortcut is a way to reach an exact answer in your head with fewer steps than the usual method. It works by spotting something special about the numbers. Take 46 × 5. Five is half of ten, so work out 46 × 10 = 460 and then halve it. The answer is 230.

Every level of Shortcuts

Example: 85², a square ending in 5

85² is read “85 squared” and means 85 × 85, a number multiplied by itself.
Cover the final 5 and keep the 8 in front of it. Multiply that 8 by the next number up: 8 × 9 = 72.
Write 25 straight after the 72, which gives 7225.
So 85² = 7225, and 7225 is what you type.

Learn it step by step

Multiplying by eleven looks like work and is almost none, once you see what eleven is doing.

Take 43 × 11. Pull the digits apart — 4 and 3 — and drop their sum in the gap between them: 4, then 4+3=7, then 3. The answer is 473. Try 52 × 11: 5, then 7, then 2, so 572.

Why does it work? Because 43 × 11 is 43 × 10 + 43. Multiplying by ten shifts every digit one place left, and adding the original back puts each digit next to its neighbour — which is exactly the sum you are dropping in the middle.

The one case to watch is when the middle sum is ten or more, like 87 × 11: 8, then 15, then 7. The extra ten carries left, so 8+1=9, and the answer is 957.

Split the digits, add them, drop the total in the middle, carry if it spills, and type the answer.

Tips and common mistakes

For a pair like 57 × 63, find the round number in the middle, 60. Square it, then take away the gap squared: 3600 − 9 = 3591.
A common slip is stopping a digital root too early. The digits of 8976 add up to 30, which has two digits, so add again: 3 + 0 = 3.
Point to a two-digit date on a calendar, such as 27, and race each other to multiply it by 11. Then check on a calculator: 27 × 11 = 297.

How to play

Each level sets problems chosen so one trick works, such as 78 × 11, 95² or 64 × 76, and your rival sees the same one. Type the whole answer on the keypad, from one digit for a digital root to five digits for 125². Get it in first and Pea Pod strikes, harder the sooner you answer.

— Quick answers —

Shortcuts: the short FAQ

What is a digital root?: A digital root is the single digit you end up with when you add a number’s digits, then add the digits of that total, until one digit is left. For 5274, 5 + 2 + 7 + 4 = 18 and 1 + 8 = 9, so its digital root is 9. It also equals the remainder after dividing by 9, with one twist: when 9 divides a number exactly, its root is 9, not 0.
How do you multiply by 25 in your head?: Multiply by 100 first, then divide by 4, because 25 is a quarter of 100. For 48 × 25, that gives 4800, and a quarter of 4800 is 1200. Dividing by 4 is easiest as halving twice: 4800, then 2400, then 1200. The same idea handles × 50, which is × 100 followed by a single halving.
Which fast multiplication tricks should you learn first?: Start with the tricks that swap one hard step for an easy one: × 5 as × 10 then halve, and the multiply by 11 trick for two-digit numbers. Then move on to squares ending in 5, and to pairs around a round number, such as 48 × 52 = 2500 − 4 = 2496. Each trick fits in one sentence, which makes it easy to keep.
Why does my child struggle with mental math?: Many children struggle because they try to run the written method in their head and lose track of the carried digits. Mental arithmetic tricks replace that with steps that are easy to hold, such as × 10 and then halve. Before your child calculates, ask them to name the pattern first: a 5 at the end, an 11, or two numbers either side of a round one.
Can I use this mental math game in class, and is it free?: Yes to both: all five trick levels run free in a web browser, with no install and no login. In class, write 15², 25², 35² and 45² on the board with their answers, 225, 625, 1225 and 2025, and ask pupils to find the pattern. Then let them predict 55² before anyone multiplies. For whole classes, the schools plan is priced per pupil and gives the teacher one dashboard to see who is getting better.

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