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.
- 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
- 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
- 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
- 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
- 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
The web
Connected ideas
Follow a connection when you’re curious — some lead into completely different areas.
Four operations
Builds on
Properties of numbersCommutative, associative and distributive properties are the shortcuts behind fast, accurate calculation.
Helps you understand
Order of operationsOnce each operation is reliable, the next question is which one to do first when several appear together.
Helps you understand
Prime and composite numbersTesting whether a number is prime is just careful division: does anything divide it exactly?
Helps you understand
Data handlingFinding a mean means adding every value and dividing by how many there are.
Used inanother area
ElectricityAn electricity bill is units × rate per unit, plus fixed charges, minus subsidies — all four operations in one sheet of paper.
Usesanother area
GravityWeight 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
additionaddendsumsubtractiondifferencemultiplicationproductequal groupsarraydivisionsharinggrouping+59 more