To divide a quantity in a given ratio, add the parts of the ratio together to find the total number of parts, then divide the quantity by that total to find the value of one part. Finally, multiply one part's value by each ratio number to find each share.
Quantity ÷ Total Parts = Value of 1 Part
Example 1: Divide £60 in the ratio 1:2
Step 1
Total parts = 1 + 2 = 3
Step 2
One part = £60 ÷ 3 = £20
Step 3
Shares: 1 × £20 = £20 and 2 × £20 = £40
Step 4
Check: £20 + £40 = £60 ✔
Example 2: Share 120 sweets in the ratio 3:5
Step 1
Total parts = 3 + 5 = 8
Step 2
One part = 120 ÷ 8 = 15
Step 3
Shares: 3 × 15 = 45 and 5 × 15 = 75
Step 4
Check: 45 + 75 = 120 ✔
✓ Quick Check 1 — The Share Method
Question 1 of 10
Three-Part Ratios
The same method works with three (or more) parts — just add all parts together.
Example 3: Divide £360 between Alice, Bob, and Carol in the ratio 2:3:4
⚠ Common mistake: Don't just divide by one of the ratio numbers. Always add all parts first, then divide the total by that sum.
✓ Quick Check 2 — The Method and Checking Your Answer
Question 1 of 10
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 3 — 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 4 — 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.