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Mental arithmetic

Add, subtract, multiply and divide in your head, from 3 + 4 upward, with a clock that tightens and numbers that never stop growing.

  • Calculation
  • Timed
  • Endless levels

How it plays

A sum appears; answer it before the bar runs out. Pick from the options with the number keys, or switch to typing in the settings for the harder, honest version — options let you check rather than compute.

Each level turns one notch on one dial: a new operation, a digit more, a longer chain, or less time. There is no last level: the digits keep growing.

Four formats: solve it, find the missing number, judge a stated answer true or false, or pick every expression that equals a target. Wrong options are the mistakes people actually make — the dropped carry, the borrow taken the wrong way, the answer one ten out.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

Practice makes the arithmetic you practise faster and more accurate. It does not, on the evidence, make you better at things that are not arithmetic.

Learn

How to get better at mental arithmetic: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Read the operation first, then the sizes. 38 + 47 and 38 × 47 look alike for a moment and are worlds apart.
  2. Work from the left, the biggest part first: 38 + 47 is 38 + 40 = 78, then + 7 = 85. The leading digits come out first, so you know the answer’s size before you finish.
  3. Hold one running number, never a column of them. Each step folds into the one total you are carrying.
  4. With options shown, estimate before you look: 38 + 47 is “about 85, ends in 5”. Then pick the option that has both, rather than checking each one.

Techniques and tricks

  • Round and compensate

    Push a number to a round one, then undo the push.

    e.g. 46 + 39 = 46 + 40 − 1 = 85; 83 − 28 = 83 − 30 + 2 = 55

  • Split by place value

    Break the smaller number into tens and ones and add each in turn, tens first.

    e.g. 256 + 137 = 256 + 100 + 30 + 7 = 393

  • Subtract by counting up

    Find the gap from the smaller number to the larger, in friendly jumps.

    e.g. 1,000 − 368: 368 → 400 is 32, 400 → 1,000 is 600, so 632

  • Last-digit check

    The last digit of the answer depends only on the last digits of the numbers. Use it to rule options out instantly.

    e.g. 47 × 38 must end in 6, because 7 × 8 = 56

  • Multiply in parts

    Split one factor into tens and ones and add the two products.

    e.g. 47 × 6 = 40 × 6 + 7 × 6 = 240 + 42 = 282

  • Halve and double

    Halve one factor and double the other; the product does not change. Repeat until it is easy.

    e.g. 16 × 35 = 8 × 70 = 560

  • Divide as a missing factor

    Turn a division into “what times the divisor gives this?”, and build the answer from the left.

    e.g. 2,856 ÷ 7: 7 × 400 = 2,800, 7 × 8 = 56, so 408

As the levels climb

  • The operations arrive in order — +, then −, then ×, then ÷. When a new one appears, expect a dip: the new sign is slower than the old ones for a few checks, and that is fine.
  • Digits grow without end. Past three digits, stop carrying the whole number and carry it in chunks you can say: “four thousand, two hundred and sixty”.
  • Chains of three to five terms come in for + and −. Add as you read, left to right; never try to remember the terms and add them at the end.
  • Later levels shrink the clock to about half. When the time tightens, lean harder on estimation and the last digit: on options, the size and the final digit together almost always pick the answer.

Traps to avoid

  • The dropped carry: 47 + 38 answered as 75. The tens digit looks plausible, the units are right — check the size: 40 + 30 is already 70, and 7 + 8 makes another ten.
  • The borrow taken the wrong way: 52 − 17 answered as 45, by doing 7 − 2 in the units. If the unit on top is smaller, you must borrow; the answer’s last digit is 52’s minus 17’s plus ten.
  • One ten out: 85 offered beside 75 and 95. These come from a slip in the tens column, so check the tens with a rough sum before committing.
  • The swapped operation: 12 × 4 answered as 16. Re-read the sign whenever an answer feels too easy.

How to practise

  • Turn on “Type the answer” once options feel easy. Options let you recognise the answer; typing makes you produce it, which is the skill.
  • Practise one operation at a time in the settings when one of them lags, then mix them back in.
  • Ten minutes a day beats an hour once a week: arithmetic speed is built from many short sittings.
  • When a wrong answer shows its working, read it — the working is the method, and copying it is how the method becomes yours.

Levels

Each question has a clock that comes from the work it asks for. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More calculation

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