2
Different ways to share 24
Discover Mathematics P3: Term 2, Lessons 91–100
GoalFind all the ways to share 24 equally and see which numbers of groups work.
New words
equal groups · groups with the same number in eachfactor pair · two numbers that multiply to make a numberarray · things set in equal rows and columns
Explanation
A number can often be shared in many ways. Let us try 24. Share 24 into 2 equal groups: 24 ÷ 2 = 12. Into 3 groups: 24 ÷ 3 = 8. Into 4 groups: 24 ÷ 4 = 6. Into 6 groups: 24 ÷ 6 = 4. Into 8 groups: 24 ÷ 8 = 3. Into 12 groups: 24 ÷ 12 = 2. Each way gives a factor pair, such as 3 × 8 = 24, and it also gives an array of 24 with 3 rows of 8. But some numbers do not work. If we share 24 among 5 children, 5 × 4 = 20 is too little and 5 × 5 = 25 is too much, so there is no whole-number share. Sharing must use all 24 with none left over.
| Equal groups | In each group | Equation |
|---|---|---|
| 2 | 12 | 24 ÷ 2 = 12 |
| 3 | 8 | 24 ÷ 3 = 8 |
| 4 | 6 | 24 ÷ 4 = 6 |
| 6 | 4 | 24 ÷ 6 = 4 |
| 8 | 3 | 24 ÷ 8 = 3 |
| 12 | 2 | 24 ÷ 12 = 2 |
Worked examples
Share 24 counters into 4 equal rows. Each row has 6 counters, so 24 ÷ 4 = 6 and 4 × 6 = 24.
Hana has 24 eggs. She can pack them 8 in a tray and get 3 trays. She can also pack 6 in a box and get 4 boxes, or 12 in a crate and get 2 crates.
| Friends | Stickers each | Used |
|---|---|---|
| 5 | 4 | 20 (4 left) |
| 5 | 5 | 25 (too many) |
Class activity
Bean shares. Take 24 beans or buttons. Share them into equal groups in as many ways as you can and write each as a division, like 24 ÷ 3 = 8. Which numbers of groups work? Try 5 and 7 groups too. What happens?
Practice
1
What is 24 ÷ 3?
24 ÷ 3 = 8, because 3 × 8 = 24.
2
24 pencils are shared equally among 6 children. How many does each child get?
24 ÷ 6 = 4 pencils.
3
The array shows 24 dots in rows of 8. How many rows are there? Write a multiplication and a division.
There are 3 rows. 3 × 8 = 24 and 24 ÷ 8 = 3.
4
Can 24 sweets be shared equally among 5 children with none left over? Explain.
No. 5 × 4 = 20 is too few and 5 × 5 = 25 is too many, so 24 is not shared equally by 5.
5
Write all the factor pairs of 24 (multiplications with the product 24).
1 × 24, 2 × 12, 3 × 8 and 4 × 6.