Exact and Inexact Divisions — Primary and Secondary
Practise exact and inexact divisions with 1, 2 and 3-digit dividends. The exam works on division as the inverse of multiplication and prepares students for quotients, remainders, lowest common multiple and highest common factor in Secondary.
Division is the inverse operation of multiplication: sharing a quantity into equal parts. Dividing 12 by 3 means asking how many times 3 fits into 12. It is one of the operations pupils find hardest in Primary school, but it becomes easy once the times tables are well learned.
There are two kinds: exact division (no remainder, like 12÷3=4) and inexact division (with a remainder, like 13÷3=4 remainder 1). Understanding the quotient and the remainder is the basis for later Secondary concepts such as the greatest common divisor, the lowest common multiple and fractions.
With the games below you will practise divisions with 1, 2 and 3-digit dividends, of increasing difficulty. The best way to lose the fear of dividing without a calculator.
Revise the subject with our interactive games and exams:
10 operations of increasing difficulty, graded at the end. It measures your speed and accuracy.
Play →Combine the cards with the operations to reach the target number. Mental arithmetic turned into a puzzle.
Play →Navigate a grid of operations and reach the goals with the exact score.
Play →Mathematics · Primary, Secondary
Understanding division as "how many times does it fit" or "how much does each person get" makes it intuitive. The exam uses sharing contexts before moving to abstraction.
Inexact division gives a quotient and remainder. 17÷5=3 remainder 2 (because 5×3=15, and 17-15=2). Mastering this is essential for fractions and decimals.
If 6×7=42, then 42÷6=7 and 42÷7=6. Seeing the relationship between multiplication and division halves calculation time.
"A Year 5 student who made errors in long division learns to verify: multiply the quotient by the divisor and add the remainder — it must equal the dividend. A check that eliminates 90% of mistakes."
Tricks and techniques to master this topic faster:
Verification rule: dividend = (quotient × divisor) + remainder. If 47÷6=7 r5: 7×6+5=47. Always check this way.
Dividing by 2: if the number is even, the result is exact. 86÷2=43. If odd, remainder is 1: 87÷2=43 r1.
Divisibility rules: divisible by 3 → digit sum divisible by 3. By 5 → ends in 0 or 5. By 10 → ends in 0.
For Secondary: HCF (Highest Common Factor) is found with the Euclidean algorithm. LCM is found by prime factorisation.
If you are studying Division — Maths Exam, these curriculum topics complement each other:
Tuthor uses essential cookies to work and, with your permission, analytics cookies to improve the experience.