Simplifying a ratio means dividing both sides by the same number until nothing further will divide them. The largest number that does the job in one go is their greatest common divisor, so 18:24 reduces to 3:4 after dividing both by 6. The proportion is untouched; only the size of the numbers changes.
The unit form, where one side is forced to 1, is often more useful than the tidy whole-number form. A gear ratio of 3:4 is also 1:1.333, and that decimal is what you multiply by. Engineers and cooks tend to think in unit ratios for exactly that reason, even when the reduced form looks neater.
The formula
a- The first term
b- The second term
g- Their greatest common divisor
a ÷ b- The decimal equivalent of the ratio
How it works, step by step
- Enter the first term of your ratio.
- Enter the second term.
- The gauge shows the decimal value of a divided by b.
- Read the simplified whole-number ratio and the unit forms below.
Worked examples
Simplifying 18:24
The greatest common divisor of 18 and 24 is 6, so dividing both sides gives 3:4. As a decimal that is 0.75, unchanged by the simplification.
A mix specified as 350:1400
The divisor is 350, reducing the ratio to 1:4. In unit form that is 1:4, which is the number you multiply the first quantity by.
How to read your score
Frequently asked questions
Why divide by the greatest common divisor rather than repeatedly by 2 or 3?
Both reach the same answer, but the greatest common divisor gets there in one step. Repeated halving only works while both sides stay even.
Can a simplified ratio contain decimals?
The whole-number form should not. If your inputs are decimals, scale both up by the same power of ten first — 1.5:2.5 becomes 15:25, which reduces to 3:5.
What does a ratio of 1:1 mean?
Equal parts. Any ratio where the two terms are the same reduces to 1:1, whether it started as 7:7 or 250:250.
Is a ratio the same as a fraction?
Closely related but not identical. The ratio 3:4 corresponds to the fraction 3/7 of the total, because a ratio compares parts to each other while a fraction compares a part to the whole.
Ratios and their lowest terms
| First term | Against 24 | GCD | Lowest terms | Decimal |
|---|---|---|---|---|
| 4 | 4:24 | 4 | 1:6 | 0.1667 |
| 6 | 6:24 | 6 | 1:4 | 0.2500 |
| 9 | 9:24 | 3 | 3:8 | 0.3750 |
| 12 | 12:24 | 12 | 1:2 | 0.5000 |
| 15 | 15:24 | 3 | 5:8 | 0.6250 |
| 18 | 18:24 | 6 | 3:4 | 0.7500 |
| 24 | 24:24 | 24 | 1:1 | 1.0000 |
| 36 | 36:24 | 12 | 3:2 | 1.5000 |
| 45 | 45:24 | 3 | 15:8 | 1.8750 |
Every row is divided by its own greatest common divisor with 24.