Mental maths

Mental maths is not a talent you either have or don't. It's a handful of tricks that skilled calculators use as a matter of course. Once you know them, laborious working turns into a few quick, confident steps.

Split by place value

Big numbers look intimidating but are just building blocks. For $47 + 36$ you first do the tens, $40 + 30 = 70$, then the ones, $7 + 6 = 13$, and put them together: 83. Each single step is small enough to do safely in your head.

Anchor at round numbers

Round numbers like 10, 50 or 100 are handy stepping stones. Instead of grinding through $26 + 9$, use that 9 is nearly 10: work out $26 + 10 = 36$ and take 1 back off, because you added 1 too many. Result: 35. The same trick helps when multiplying, only the correction gets multiplied too: do $4 \cdot 19$ as $4 \cdot 20 = 80$ and take $4 \cdot 1 = 4$ back off, which leaves 76.

Doubling and halving

Some calculations get easy if you double one number and halve the other, the product stays the same. For $5 \cdot 18$ you'd rather do $10 \cdot 9 = 90$. And $12 \cdot 25$ becomes $6 \cdot 50 = 300$. Halving and doubling pair perfectly with the handy numbers 10, 50 and 100.

Estimate as a check

Before you trust a result, estimate roughly: $198 + 47$ is close to $200 + 50 = 250$. If your exact answer lands nearby, it's probably right. If it's far off, you slipped somewhere. That way you catch mistakes before they cost you.