EARLY OPERATIONS · TEXTBOOK LESSON
Division separates a quantity into equal groups or finds how many groups of a given size fit into a quantity. It is the inverse of multiplication.
Learning objectives
By the end of this lesson, you should be able to:
- Interpret division as sharing and grouping.
- Use multiplication facts to derive division facts.
- Calculate quotients using mental or written methods.
- Interpret remainders correctly in context.
1. Key vocabulary and definition
Definition
In a ÷ b = c, a is the dividend, b is the divisor and c is the quotient. A remainder is what is left when the dividend is not an exact multiple of the divisor.
dividenddivisorquotientremainderinverse
2. Essential facts and rules
These are the facts you should know before attempting the worked example.
Key mathematical facts
- If 6 × 8 = 48, then 48 ÷ 6 = 8 and 48 ÷ 8 = 6.
- Division by 1 leaves a number unchanged.
- Division by zero is undefined.
3. Standard method
A reliable method helps prevent errors and makes your reasoning easy to follow.
1
Estimate the size of the quotient.
2
Use known multiplication facts or a written division method.
3
Record any remainder carefully.
4
Decide whether the remainder should stay as a remainder, become a fraction/decimal, or cause rounding up in context.
5
Check by multiplying divisor × quotient and adding any remainder.
4. Worked example
Worked example
Calculate 157 ÷ 12.
1
12 × 13 = 156.
2
157 - 156 = 1.
3
Therefore 157 ÷ 12 = 13 remainder 1.
4
Check: 12 × 13 + 1 = 157.
5. Common mistakes
Watch out for these
- Starting calculations before deciding what the question is asking.
- Skipping important steps or changing notation midway through a solution.
- Accepting an answer without checking whether its size, sign or unit is sensible.
6. Video lesson
This topic is ready for a matching video lesson. The written textbook lesson is fully available now; additional videos can be added to the same lesson template.
7. Practice exercise
Complete these without looking at the answers first.
- Calculate 42 ÷ 6.
- Calculate 96 ÷ 8.
- Calculate 73 ÷ 5 and give a remainder.
- 24 sweets are shared equally among 6 children. How many each?
- 95 people need minibuses holding 12 people each. What is the minimum number of minibuses?
Show answers
- 7
- 12
- 14 remainder 3
- 4 sweets
- 8 minibuses
8. Chapter summary
- Understand the underlying idea before memorising a procedure.
- Use precise mathematical notation and show a logical method.
- Always check the final result.