LEARN · PRACTISE · DISCOVER
What Is Division? Sharing and Grouping
You have 12 cookies and 3 friends. How can you share them fairly? This is a job for division. Division means splitting a total into equal parts. In this lesson you will learn the two ways to think about division and how to write it.
Division as sharing
Sharing means giving out a total equally to a set number of groups. You know how many groups, and you want to find how many go in each group.
Example
Share 12 cookies equally between 3 friends. Give one cookie to each friend, then another, and keep going until the cookies run out. Each friend gets 4 cookies.
We write: 12 ÷ 3 = 4
Division as grouping
Grouping means making groups of a set size. You know how many go in each group, and you want to find how many groups you can make.
Example
You have 12 cookies and want to put 4 cookies on each plate. How many plates do you need? Make groups of 4: one plate, two plates, three plates. You need 3 plates.
We still write: 12 ÷ 4 = 3
| Type | What you know | What you find | Example |
|---|---|---|---|
| Sharing | number of groups | how many in each | 15 sweets shared by 5 children: 3 each |
| Grouping | size of each group | number of groups | 15 sweets in bags of 5: 3 bags |
Division words
In a division sentence like 20 ÷ 4 = 5:
- 20 is the dividend, the total being divided.
- 4 is the divisor, the number you divide by.
- 5 is the quotient, the answer.
The symbol ÷ is read “divided by”. Division problems often use words like share, split, each, equal groups and per.
Division as repeated subtraction
Another way to divide is to keep subtracting the same number until you reach zero. For 15 ÷ 5: 15 − 5 = 10, 10 − 5 = 5, 5 − 5 = 0. You subtracted 5 three times, so 15 ÷ 5 = 3.
Division undoes multiplication
Multiplication puts equal groups together. Division splits a total into equal groups. They are opposites! If you know 4 × 5 = 20, you can work out that 20 ÷ 5 = 4 and 20 ÷ 4 = 5. You will explore this in the next lesson.
Dividing by 1 and by itself
- Any number divided by 1 is itself: 9 ÷ 1 = 9.
- Any number (except 0) divided by itself is 1: 9 ÷ 9 = 1.
- We cannot divide by 0. You cannot share things into zero groups!
Key takeaways
- Division splits a total into equal parts.
- Sharing finds how many in each group; grouping finds how many groups.
- In 20 ÷ 4 = 5, the answer 5 is the quotient.
- Division is the opposite of multiplication.
Practice
- Share 18 stickers equally among 3 children. How many each?
- 24 eggs are packed in boxes of 6. How many boxes?
- What is 7 ÷ 7?
Answers: 1 is 18 ÷ 3 = 6 each. 2 is 24 ÷ 6 = 4 boxes. 3 is 1.