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Mathematics · Numbers

Four operations

When should you add, subtract, multiply or divide — and how do you know your answer makes sense?

Addition, subtraction, multiplication and division with large numbers, choosing the right operation in real problems, and checking answers by estimating and by inverse operations.

5 depths≈ 230 min of reading74 practice questions

The ladder

Choose how deep to go

Every depth is open. Start where it feels interesting — you can always move back.

  1. Discoverabout 35 minFour ways to change a numberMeet the four operations through a kirana-shop trip, cricket scores, egg trays and shared laddoos. Learn what each operation means, how they undo each other, how to pick the right one from a story, and how to check that an answer is sensible.Owner-accepted · not line-by-line reviewed
  2. Understandabout 45 minHow the column methods workLearn the exact name for every part of a calculation, then master column addition and subtraction up to crores, long multiplication, long division with remainders and zeros in the quotient, checking with inverse operations, and working with money and units.Owner-accepted · not line-by-line reviewed
  3. Investigateabout 45 minPredict, test, checkPredict before you calculate and test with labs and tables: estimate sums and products, see what happens when numbers change, decide what a remainder means in a story, catch misleading keywords and check answers by undoing them.Owner-accepted · not line-by-line reviewed
  4. Go deeperabout 55 minWhy the methods workProve why carrying, borrowing, long multiplication and long division work, meet the division algorithm and why dividing by zero is impossible, check with casting out nines, use the unitary method wisely, and solve India-sized multi-step problems.Owner-accepted · not line-by-line reviewed
  5. Extendabout 50 minOther ways to calculate, and harder puzzlesTry the lattice, Napier's bones, Vedic-style shortcuts and Russian peasant multiplication and see why each works. Crack classic puzzles and olympiad problems, then plan real projects: a trip budget, a kirana bill, a harvest and a run chase.Owner-accepted · not line-by-line reviewed

Practise and apply

Question bank · 74 questions

8 sections from Foundation to Challenge, each with hints and a worked solution — or play a 10-question round for points and stars.

Foundation 15Core 29Stretch 22Challenge 8

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The web

Connected ideas

Follow a connection when you’re curious — some lead into completely different areas.

Four operations

  • Builds on

    Number system

    Place value is what makes column addition, carrying and long division work.

  • Builds on

    Properties of numbers

    Commutative, associative and distributive properties are the shortcuts behind fast, accurate calculation.

  • Helps you understand

    Order of operations

    Once each operation is reliable, the next question is which one to do first when several appear together.

  • Helps you understand

    Prime and composite numbers

    Testing whether a number is prime is just careful division: does anything divide it exactly?

  • Helps you understand

    Data handling

    Finding a mean means adding every value and dividing by how many there are.

  • Used inanother area

    Electricity

    An electricity bill is units × rate per unit, plus fixed charges, minus subsidies — all four operations in one sheet of paper.

  • Usesanother area

    Gravity

    Weight on another world is your mass times that world's gravity — multiplication with an astonishing answer.

Words to know

71 words are explained in these lessons

All vocabulary →

additionaddendsumsubtractiondifferencemultiplicationproductequal groupsarraydivisionsharinggrouping+59 more