1
Dividing counters into fractions
Discover Mathematics P3: Term 2, Lessons 71–80
GoalFind a fraction of a group by dividing it into equal groups, including fractions such as 3/4 and 2/3.
New words
equal groups · groups that have the same number of thingsfraction of a set · a part of a group of thingscounters · small objects used for counting and sharing
Explanation
To find a fraction of a group, divide the group into equal groups. The bottom number of the fraction tells how many equal groups to make. Each group is a unit fraction of the whole group. For 12 counters, 1/4 means 4 equal groups: 12 ÷ 4 = 3, so 1/4 of 12 is 3. The top number tells how many groups to take. So 3/4 of 12 is 3 groups of 3, which is 3 × 3 = 9. For thirds, share into 3 groups: 1/3 of 12 is 4 and 2/3 of 12 is 2 × 4 = 8. Check by adding all the parts: 4 + 4 + 4 = 12.
Worked examples
Divide 12 counters into 4 equal groups. There are 3 counters in each group, so 1/4 of 12 is 3.
Divide 12 counters into 3 equal groups. There are 4 counters in each group, so 1/3 of 12 is 4. Two groups make 2/3 of 12, which is 8.
| Fraction | Work | Apples |
|---|---|---|
| 1/2 | 12 ÷ 2 | 6 |
| 1/3 | 12 ÷ 3 | 4 |
| 1/4 | 12 ÷ 4 | 3 |
| 1/6 | 12 ÷ 6 | 2 |
| 3/4 | 3 × 3 | 9 |
Class activity
Apple shares. Take 12 small objects such as beans or buttons. Find 1/2, 1/3, 1/4 and 1/6 of them by making equal groups. Then find 2/3 and 3/4. Write each answer as a sentence, such as: 2/3 of 12 is 8.
Practice
1
Find 1/3 of 18 counters.
18 ÷ 3 = 6, so 1/3 of 18 is 6.
2
Find 1/4 of 20 stickers.
20 ÷ 4 = 5, so 1/4 of 20 is 5 stickers.
3
The apples are in 3 baskets with the same number in each. Karim takes 2 of the baskets. What fraction of the apples is that, and how many apples?
He takes 2/3 of the apples. There are 4 apples in a basket, so 2 baskets have 2 × 4 = 8 apples.
4
Find 3/4 of 16.
16 ÷ 4 = 4, and 3 × 4 = 12. So 3/4 of 16 is 12.
5
Habiba has 12 stickers and gives 1/6 of them to her cousin. How many stickers does she give?
12 ÷ 6 = 2 stickers.