Maths
What is division?
Quick answer
Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.
In one sentence
Division means splitting a number into equal groups and finding how many are in each group, or how many groups there are.
Explained
Division can mean two slightly different things.
Sharing. Twelve cookies are shared fairly between 3 plates. How many on each plate? Deal them out one at a time and each plate gets 4. So 12 ÷ 3 = 4.
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Grouping. You have 12 cookies and want to pack them in bags of 3. How many bags? Keep taking out 3 until none are left: 4 bags. Same calculation, different story.
Division is the inverse of multiplication. If you know 6 × 7 = 42, you also know 42 ÷ 7 = 6 and 42 ÷ 6 = 7. That is why knowing your times tables makes division fast.
Sometimes things don't share out exactly. 14 ÷ 4 is 3, with 2 left over, written 3 r 2. Depending on the problem, you might round up (you need 4 boxes for 14 cakes if a box holds 4), round down (you can make 3 full teams), or split the leftover into a fraction: 3½.
Order matters: 12 ÷ 3 is 4, but 3 ÷ 12 is a quarter. Dividing by 0 has no answer at all.
Examples
- 15 ÷ 5 = 3 (because 5 × 3 = 15)
- 100 ÷ 10 = 10
- 23 ÷ 4 = 5 r 3 (4 × 5 = 20, 3 left over)
- 96 ÷ 4: split 96 into 80 + 16. 80 ÷ 4 = 20, 16 ÷ 4 = 4, so 24.
- 732 ÷ 6 by short division: 7 ÷ 6 = 1 r 1; 13 ÷ 6 = 2 r 1; 12 ÷ 6 = 2. Answer 122.
Common mistakes
- Dividing the wrong way round, so 4 ÷ 20 is treated like 20 ÷ 4. Fix: read it as "4 shared between 20 people".
- A remainder bigger than the divisor, like 17 ÷ 5 = 2 r 7. Fix: if the leftover is 5 or more, another group fits.
- Ignoring what the remainder means in word problems. Ask "what happens to the leftovers?"
Quick quiz
Division
Check what you know with 4 quick questions.
Question 1 of 4
20 sweets are shared equally between 4 children. How many does each get?
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Division worksheets
For grown-ups
Related topics
Multiplication
Multiplication is adding equal groups quickly. 4 × 3 means 4 groups of 3 (or 3 groups of 4), which makes 12. The answer is called the product.
Times tables
Times tables are lists of the multiplication facts for a number, such as 3 × 1 = 3 up to 3 × 12 = 36. Knowing them by heart speeds up almost all later maths.
Fractions
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
Factors and multiples
Factors are numbers that divide exactly into a number (the factors of 12 are 1, 2, 3, 4, 6 and 12). Multiples are the numbers in its times table (12, 24, 36…).
Odd and even numbers
Even numbers can be split into two equal groups or pairs with none left over (2, 4, 6…). Odd numbers always leave one left over (1, 3, 5…).
Prime numbers
A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13.