Maths⏱ 4 min read
How to Simplify a Ratio and Scale It Up or Down
Ratios appear in recipes, concrete mixes, map scales, and financial analysis. Here is how to simplify any ratio, find the missing value, and use ratios to divide quantities.
A ratio expresses a relationship between two quantities. The maths is simple but misapplied surprisingly often — especially when scaling recipes or mixing materials.
Simplifying a Ratio
Divide both numbers by their Greatest Common Factor (GCF)
Ratio 24:36
Factors of 24: 1,2,3,4,6,8,12,24
Factors of 36: 1,2,3,4,6,9,12,18,36
GCF = 12
Simplified: 24/12 : 36/12 = 2:3
Ratio 150:250:
GCF of 150 and 250 = 50
Simplified: 3:5
Quick method: keep dividing by common factors
60:90 → 30:45 (÷2) → 6:9 (÷5) → 2:3 (÷3)
Scaling a Ratio
To scale a ratio, multiply both parts by the same number.
Concrete mix 1:2:3 (cement:sand:aggregate) for 1 batch.
For 7 batches: multiply all parts by 7
= 7:14:21
Recipe calls for flour:butter 3:2
To make using 450g flour:
Scale factor = 450 / 3 = 150
Butter needed: 2 x 150 = 300g
Map scale 1:25,000
Distance on map: 4.5cm
Real distance: 4.5 x 25,000 = 112,500cm = 1.125km
Dividing a Quantity in a Given Ratio
Share £480 between two people in ratio 3:5
Total parts: 3 + 5 = 8 parts
Value of one part: £480 / 8 = £60
Person A (3 parts): 3 x £60 = £180
Person B (5 parts): 5 x £60 = £300
Check: £180 + £300 = £480 ✓
Three-way ratio: share 720 in ratio 2:3:4
Total parts: 2+3+4 = 9
One part = 720/9 = 80
Shares: 160, 240, 320
Check: 160+240+320 = 720 ✓
Finding a Missing Value
If ratio is 4:7 and one quantity is 28, find the other.
Method: 4/7 = ?/28
Cross multiply: 4 x 28 = 7 x ?
112 = 7 x ?
? = 16
Or: scale factor = 28/7 = 4
Other quantity = 4 x 4 = 16
Checking: 16:28 = 16/4 : 28/4 = 4:7 ✓
Practical example:
Mixing squash, ratio 1 part concentrate to 4 parts water.
Using 250ml concentrate — how much water?
? = 250 x 4 = 1,000ml water
Total drink: 1,250ml
Ratio vs Fraction vs Percentage
These are equivalent ways of expressing the same relationship:
Ratio 1:4 → fraction 1/5 of total → 20% of total
Ratio 2:3 → fraction 2/5 of total → 40% of total
(The first quantity is 40% of the combined total)
Converting ratio to percentage:
2:3 → total parts = 5
First part as percentage = 2/5 x 100 = 40%
Second part: 3/5 x 100 = 60%