Sharing in a Ratio
Sharing in a ratio helps us divide a quantity into proportional parts. It’s a key skill for everything from mixing ingredients in a recipe to splitting prize money fairly with friends.
The 4-Step Method for Sharing in a Ratio
To share an amount in a given ratio, follow these simple steps. Let’s imagine we’re sharing 10 sweets in the ratio $2:3$.
1. Add the Parts
First, find the total number of parts by adding the numbers in the ratio.
$2 + 3 = 5$ total parts.
2. Divide the Total
Divide the total amount by the total number of parts to find the value of one part.
$10 \div 5 = 2$ sweets per part.
3. Multiply for Each Share
Multiply the value of one part by each number in the ratio.
Share 1: $2 \times 2 = 4$
Share 2: $3 \times 2 = 6$
4. Check Your Answer
Add the shares together to make sure they equal the original total amount.
$4 + 6 = 10$. Correct!
Visualising with a Bar Model
A bar model makes it easy to see the ‘parts’. For a ratio of $2:3$, we have 5 parts in total. Each part is worth 2 sweets.
Worked Examples
Example 1: Sharing Money
Sarah and Tom share £80 in the ratio $3:5$. How much does each person receive?
- Total parts: $3 + 5 = 8$ parts.
- Value of one part: £80 ÷ 8 = £10.
- Calculate shares:
Sarah (3 parts): $3 \times £10 = £30$
Tom (5 parts): $5 \times £10 = £50$ - Check: £30 + £50 = £80.
Answer: Sarah gets £30, Tom gets £50.
Example 2: Mixing Ingredients
A baker makes 600g of pastry using flour, butter, and water in the ratio $8:4:3$. How much of each ingredient is needed?
- Total parts: $8 + 4 + 3 = 15$ parts.
- Value of one part: 600g ÷ 15 = 40g.
- Calculate shares:
Flour (8 parts): $8 \times 40g = 320g$
Butter (4 parts): $4 \times 40g = 160g$
Water (3 parts): $3 \times 40g = 120g$ - Check: 320g + 160g + 120g = 600g.
Tutor Insights
🤔 Common Misunderstandings
- Not finding the total parts: Dividing the total amount by one of the ratio numbers instead of their sum.
- Forgetting to multiply back: Finding the value of one part correctly but then stopping and not calculating the final shares.
📝 Common Exam Mistakes
- Simple arithmetic errors in addition or division.
- Answering only for one part when the question asks for all shares.
- Forgetting to include units (like £ or g) in the final answer.
Practice Questions
- Share £50 in the ratio $2:3$.
- Amy and Ben share 35 pens in the ratio $4:3$. How many pens does Ben get?
- A sum of £120 is divided between three charities in the ratio $1:2:3$. How much does each charity receive?
Show Answers
- Working: Total parts=5. One part=£50÷5=£10. Shares are $2 \times £10$ and $3 \times £10$.
Answer: £20 and £30. - Working: Total parts=7. One part=35÷7=5 pens. Ben gets 3 parts, so $3 \times 5 = 15$.
Answer: Ben gets 15 pens. - Working: Total parts=6. One part=£120÷6=£20. Shares are $1 \times £20$, $2 \times £20$, and $3 \times £20$.
Answer: £20, £40, and £60.
FAQs
What’s the difference between a ratio and a fraction?
A ratio compares parts to other parts (e.g., 2 parts red to 3 parts blue). A fraction compares a part to the whole (e.g., 2 out of 5 total parts are red). You need to add the ratio parts together to find the ‘whole’ for the fraction’s denominator.
How do I check if my answer is correct?
The best way to check is to add up all the individual shares you’ve calculated. If their sum matches the original total quantity you started with, then your answer is correct!
