⚠ Common mistake: Don't just divide by one of the ratio numbers. Always add all parts first, then divide the total by that sum.
Finding a Quantity from One Part
Sometimes you know one person's share and need to find the total or another share.
Example 4: Two friends share money in ratio 3:5. The first person gets £45. How much does the second person get?
Step 1
First person has 3 parts = £45
Step 2
One part = £45 ÷ 3 = £15
Step 3
Second person: 5 × £15 = £75
💡 Always check your answer by working backwards. If 2nd person gets £75 and ratio is 3:5, then 1st person should get (3/5) × £75 = £45. ✔
✓ Quick Check 2 — Three-Part Ratios & Finding from One Part
Question 1 of 10
Practice Problems
Work through each problem. Type your answer(s) and press Check.
Practice: Dividing in a Ratio
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Question
Answer
Result
1
Divide £80 in the ratio 3:1
A:B:
2
Divide 120 in the ratio 2:3
A:B:
3
Divide £200 in the ratio 1:3:4
A:B:C:
4
Divide 90 sweets in the ratio 2:3:5
A:B:C:
5
Divide £540 in the ratio 4:5
A:B:
6
Share 2 hours in the ratio 3:1 (give answers in minutes)
A:B:
7
Divide 60 in the ratio 1:2:3
A:B:C:
8
Divide £1000 in the ratio 3:7
A:B:
9
Divide £360 in the ratio 2:3:4
A:B:C:
10
Divide 96 in the ratio 3:5
A:B:
✓ Quick Check 3 — Mixed Ratio Division
Question 1 of 10
⚠ Things to Watch Out For
Using the ratio numbers directly as amounts: "Share £40 in ratio 3:5" — 3 and 5 are PARTS, not pounds. Find the value of one part first: £40 ÷ 8 = £5 per part.
Adding the ratio parts incorrectly: 3:5 has 3+5=8 parts total. Always add ALL parts of the ratio to find the total number of parts.
Forgetting to multiply each share: Person A gets 3 × £5 = £15. Person B gets 5 × £5 = £25. Students sometimes just write £5 without multiplying by their share.
Not checking the answer adds up: £15 + £25 = £40 ✓. Always verify the shares sum to the original total.
Three-way splits: Ratio 2:3:5 — total parts = 10. Find one part, then multiply by 2, 3, and 5 respectively. Don't forget the third person.