Mental Math: Calculate Fast in Your Head
A dozen small techniques, each backed by real maths, that replace the phone calculator for the numbers you meet every day.
For adults who reach for the calculator to work out a tip or a discount. You will learn why each shortcut works, watch it done step by step on real numbers, see the mistake people usually make, and then do enough practice to trust yourself. By the end you will add, subtract, multiply, take percentages, split bills and check your own answers without writing anything down.
By the end you can
- Add and subtract three-digit numbers in your head, left to right, without borrowing
- Multiply two-digit numbers using splitting, doubling, ×11 and the squaring tricks
- Work out any percentage, discount or bill split from 10%, 5% and 1%
- Estimate an answer before you calculate it, and check it three ways afterwards
Adding and subtracting
- Work left to right
Add and subtract two- and three-digit numbers in your head by starting with the biggest part, the way you read the number, instead of the paper method school taught you.
- Round and fix
Turn an awkward number into a round one, do the easy sum, then pay back the difference. This one habit handles every 98, 99, 197 and 499 you will ever meet.
- Subtract by adding up
Stop taking numbers away. Walk up from the smaller number to the bigger one and count the steps. It makes 1000 − 637 a three-second job and kills borrowing for good.
Multiplying
- Break it apart
Multiply a big number by splitting it into parts you already know, and learn the four shortcuts that cover most of the times table you never memorised: ×4, ×5, ×8 and ×9.
- Doubling, halving and ×11
Reshape a multiplication until it becomes easy: halve one side, double the other, and watch 16 × 25 turn into 4 × 100. Then learn the ×11 trick, carry case included.
- Squares and near-squares
Square any number ending in 5 in about two seconds, square numbers near 50 and near 100, and turn 19 × 21 into 20² − 1 without writing anything down.
Percentages, fractions and division
- Percent from building blocks
Learn three pieces by heart, 10%, 5% and 1%, and you can build any percentage you meet: 15%, 18%, 35%, 3%. No formula, no calculator, no decimals to juggle.
- The percent swap, and percent change
Two things that save you daily: x% of y is the same as y% of x, and a price that goes up then down by the same percent does not come back. Stacked discounts too.
- Division and fractions in your head
Divide by 4 and 8 with nothing but halving, turn ÷5 into a doubling, and learn the handful of fraction-to-percent pairs that make a quarter of daily arithmetic instant.
Numbers in real life
- Estimate first
Round hard, compute fast, and get an answer that's close enough to act on. Estimating is also the check that catches a mistyped calculator, which is the one error nobody notices.
- Money maths
Put the whole course to work where it pays: comparing two pack sizes, reading a real discount, splitting a bill with service on top, and spotting an offer that isn't one.
- Check yourself, and keep the skill
Three checks that catch a wrong answer in seconds, including casting out nines and what it can't see. Then a five-minute daily plan and a mixed challenge across the whole course.
Keep it, don't just read it
Pathwise brings each idea back just before you'd forget it, with a quick question. Free on Android and on the web, in English and Persian.