Ratio & Proportion Calculator
Simplify ratios, solve proportions, and divide amounts with step-by-step solutions. Perfect for GCSE and KS3 maths.
Key Formulas
Simplifying Ratios
Divide all parts by GCF
12:18 → 12÷6 : 18÷6 = 2:3
Equivalent Ratios
Multiply all parts by same number
2:3 × 4 = 8:12
Solving Proportions
a:b = c:x → x = (b×c)/a
2:5 = 6:x → x = (5×6)/2 = 15
Dividing in a Ratio
One part = Total ÷ Sum of ratio parts
£100 in ratio 2:3 → 100÷5 = £20 per part → £40:£60
Common Mistakes
Adding instead of dividing by GCF
To simplify, DIVIDE all parts by the same number
Forgetting to simplify the final answer
Always check if you can simplify further
Mixing up ratio order in word problems
Read carefully: "boys to girls" means boys:girls
Adding ratio parts incorrectly when dividing amounts
Add ALL parts: in 2:3:5, total = 2+3+5 = 10 parts
Understanding Ratios & Proportions
What is a Ratio?
A ratio compares two or more quantities. It shows the relative size of different parts. Written as 2:3 or 2 to 3, it means "2 parts to 3 parts".
Real-world examples:
- • Mixing paint: 2 parts blue to 1 part white
- • Recipe: flour to sugar is 3:1
- • Map scale: 1:50000
Ratio vs Fraction
- Ratio 2:3compares parts to parts
- Fraction 2/5shows part of the whole (2 out of 5 total)
- •To convert ratio to fraction: 2:3 means 2 out of 5 = 2/5
- •Ratios have no units - they're dimensionless
Key Ratio Operations
Simplifying Ratios
Find the GCF (Greatest Common Factor) and divide all parts by it.
12 : 18 → GCF = 6 → 2 : 3
12÷6 = 2, 18÷6 = 3
Solving Proportions
Use cross multiplication: if a:b = c:x, then a×x = b×c.
2:5 = 6:x → 2×x = 5×6 → x = 30÷2 = 15
Verify: 2:5 = 6:15 ✓ (both simplify to 2:5)
Dividing Amounts in a Ratio
Add total parts, find value of one part, then calculate each share.
£100 in ratio 2:3 → 5 parts → £20 each
Shares: 2×£20 = £40 and 3×£20 = £60
Equivalent Ratios
Multiply or divide all parts by the same number.
Scale up:
2:3 × 4 = 8:12
Scale down:
8:12 ÷ 4 = 2:3
Exam Tips
Always Simplify
Exam answers should always be in simplest form. Check if you can divide further.
Order Matters!
"Boys to girls" means boys:girls. Read the question carefully!
Add for Total Parts
When sharing, add all ratio parts first: 2:3:5 = 10 total parts.
Cross Multiply
For proportions a:b = c:d, use a×d = b×c to find unknowns.
Check Your Answer
Verify by checking shares add up to the total amount.
Same Units
Make sure both quantities have the same units before writing the ratio.
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