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Sharing by ratio
Parts and wholes, finding the total number of parts, and working backwards from a share.
Tom and Amy share some sweets, but not equally. For every 2 sweets Tom gets, Amy gets 3. That is a ratio, written 2 : 3. In this lesson you will learn how to:
- read and write a ratio, in the right order
- tell the parts from the whole
- find the total number of parts
- share an amount in a ratio, using a bar model
- work backwards when you know one share, or the difference between two shares
1. What a ratio means
Example: a bead necklace
Each group has 2 red beads and 3 blue beads. So the ratio of red to blue is 2 : 3. The necklace has 3 groups: 6 red and 9 blue. That is still 2 red for every 3 blue.
Bead maker
- Make one group: tap a bead in the tray to add it, and tap a bead in your group to take it out. Then press Check and watch the necklace grow.
- Some turns show you a necklace instead. Pick its ratio, in the right order.
2. Parts and the whole
Example: red and blue beads in the ratio 2 : 3
| Ratio of red to blue | 2 : 3 |
|---|---|
| Total number of parts | 2 + 3 = 5 |
| Fraction that are red | 25 |
| Fraction that are blue | 35 |
Sweet jar detective
- Count the sweets in the jar, then answer each question about it.
- A jar with no slips moves you up a level. Level 1 asks for the ratio and the total number of parts, level 2 adds fractions, and level 3 brings a third colour.
3. Sharing in a ratio
Example: Tom and Amy share £40 in the ratio 2 : 3
- Add the parts:2 + 3 = 5 parts
- Find one part (divide by 5):£40 ÷ 5 = £8
- Find each share (multiply):Tom: 2 × £8 = £16 Amy: 3 × £8 = £24
- Check:£16 + £24 = £40
Why divide by the total number of parts?
Share 15 sweets in the ratio 1 : 2 by dealing them out in rounds. Each round, Tom gets 1 and Amy gets 2. That uses 3 sweets a round, and 15 ÷ 3 = 5 rounds. So Tom gets 5 × 1 = 5 sweets and Amy gets 5 × 2 = 10 sweets.
Three people: 36 stickers in the ratio 1 : 2 : 3
1 + 2 + 3 = 6 parts, and 36 ÷ 6 = 6. Ali gets 6, Ben gets 12 and Cat gets 18.
Deal the sweets
- Tap the bag to deal one round. Keep going until the bag is empty.
- Then answer the questions. How many rounds did it take?
Bar model sharer
- Draw the bars first: tap the box where each person’s bar should end. Then add, divide and multiply.
- Two with no slips moves you up a level. Levels 1 and 2 share things, level 3 shares money and measures, level 4 shares between three people, and level 5 works in pence.
4. Working backwards from a share
From one share
Red and blue beads are in the ratio 2 : 3. There are 12 red beads. How many blue beads are there?
The 12 red beads fill 2 boxes, so one box is 12 ÷ 2 = 6. Blue is 3 × 6 = 18 beads. All together, 5 × 6 = 30 beads.
From the difference
Sam and Jo share sweets in the ratio 3 : 5. Jo gets 8 more than Sam. How many sweets are there?
Jo has 5 − 3 = 2 more boxes, and they hold the 8 extra sweets. So one box is 8 ÷ 2 = 4. There are 8 boxes altogether: 8 × 4 = 32 sweets.
Mystery bars
- Step 1: tap the boxes that hold the number you know. Step 2: find one box. Step 3: find the answer.
- Two with no slips moves you up a level. Level 1 finds the other share, level 2 finds the whole amount, and level 3 starts from the difference.
5. Be the teacher
Some children have answered ratio questions. Is each one right? If not, what went wrong?
6. Practice: pick your level
Start with Foundation if you are in Year 4 or just starting. Move up when you are getting most of them right.
The mistakes that cost marks
- Writing the ratio the wrong way round. Writing 2 : 3 when the question asks for blue to red. the first number goes with the first thing named: blue to red is 3 : 2.
- Dividing by the wrong number. Sharing £40 in the ratio 2 : 3 by working out £40 ÷ 2. add the parts first and divide by the total: £40 ÷ 5 = £8.
- Sharing equally. Giving Tom and Amy £20 each. a ratio of 2 : 3 is not equal shares: Tom gets 2 parts and Amy gets 3.
- Mixing up a ratio and a fraction. Saying 2 : 3 means 23 are red. there are 5 parts altogether, so 25 are red.
- Treating one share as the whole amount. Tom gets 12 in the ratio 2 : 3, and working out 12 ÷ 5. 12 is Tom’s 2 parts, so one part is 12 ÷ 2 = 6.
- Treating the difference as one part. Jo gets 8 more than Sam in the ratio 3 : 5, so one part is 8. the difference is 5 − 3 = 2 parts, so one part is 8 ÷ 2 = 4.
- Forgetting to check. Shares of £16 and £26 from £40. the shares must add up to the amount you started with.
Quick checklist
Tick each one when you can do it without help.
All ticked. Brilliant work! You have finished Lesson 4.2.
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