Learn the 3-Step Method
1Identify what the number IS.
£8 isn't the total — it's Sam's share, which is 2 parts.
2Drop to one part.
2 parts = £8 → 1 part = £4.
3Scale to what's asked.
Total 5 parts = £20; Mia's 3 parts = £12; difference = £4.
Worked Example
Tom and Jo share stickers 5 : 3. Tom has 12 MORE than Jo. How many do they have altogether?
Watch Out! Common Mistakes
Read again! £8 was SAM’S share (2 parts), so one part is £4 and the total is £20.
The difference is 2 parts! (5 − 3). 12 ÷ 2 = 6 per part → total 48.
Rebuild it! Tom 30, Jo 18: ratio 30:18 = 5:3 ✓, difference 12 ✓. If either fails, restart from ‘what does the number represent?’.
⬇ Cheat Sheet
- Ask: is the given number the total, one share, or the difference?
- Convert it to parts, then find ONE part.
- Scale to whatever is asked.
- Rebuild the story to check both facts.
📖 Continue Your Journey
Quick summary
- Decide what the given number is: total, one person's share, or the difference.
- Convert it to parts and find the value of one part.
- Scale one part to whatever the question asks for.
- Rebuild the story with your numbers to verify both facts.
Frequently asked questions
How do you solve a ratio problem when you're given one share?
Match the share to its parts: if Sam's 2 parts are £8, one part is £4, so the 5-part total is £20.
How do you use a difference in a ratio problem?
The difference corresponds to the difference in parts: sharing 5 : 3 with 12 more for the first person means 2 parts = 12, one part = 6, total 48.
What single habit solves every ratio puzzle?
Finding the value of one part first — every given (total, share or difference) converts to it, and every answer scales from it.
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