Ratio Calculator · Practical guide
How to Simplify a Ratio to Lowest Terms
Divide both terms by their greatest common divisor — 48 : 64 reduces to 3 : 4 because the GCD is 16.
At a glance
Quick answer
To simplify a ratio to lowest terms, divide both terms by their greatest common divisor (GCD) — the largest number that divides both evenly. For 48 : 64, the GCD is 16, so 48 ÷ 16 : 64 ÷ 16 gives 3 : 4. The simplified ratio has the same relationship as the original, just in its smallest whole numbers.
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Result
Step-by-Step: Simplifying 48 : 64
- Find the GCD of 48 and 64. The divisors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; the largest one that also divides 64 is 16.
- Divide both terms: 48 ÷ 16 = 3 and 64 ÷ 16 = 4.
- The result, 3 : 4, cannot be reduced further — the GCD of 3 and 4 is 1.
Common Ratios and Their Simplest Forms
| Original ratio | GCD | Lowest terms |
|---|---|---|
| 12 : 18 | 6 | 2 : 3 |
| 45 : 60 | 15 | 3 : 4 |
| 100 : 250 | 50 | 2 : 5 |
| 1920 : 1080 | 120 | 16 : 9 |
Simplifying Decimal Ratios
Clear the decimals first by multiplying both terms by the same power of 10, then reduce as usual. For 1.5 : 2.5, multiply both by 10 to get 15 : 25; the GCD of 15 and 25 is 5, giving 3 : 5. The same trick works for fractions: multiply 1/2 : 3/4 by 4 to get 2 : 3.
Why Lowest Terms Matter
Simplified ratios are the common language across contexts — the screen resolution 1920 × 1080 and the camera frame 3840 × 2160 are both 16 : 9, which you only see after dividing by 120 and 240 respectively. Enter a proportion above (for example, A = 1920, B = 1080, C = 16) and the calculator returns the simplified ratio alongside the missing value and scale factor.
Frequently Asked Questions
How do I find the GCD of two large numbers?
Use the Euclidean algorithm: repeatedly replace the larger number by the remainder of dividing the two. For 1920 and 1080: 1920 mod 1080 = 840, 1080 mod 840 = 240, 840 mod 240 = 120, 240 mod 120 = 0 — so the GCD is 120.
What if the GCD is 1?
The ratio is already in lowest terms. Ratios like 8 : 15 cannot be simplified because 8 and 15 share no divisor other than 1.
Can I simplify a ratio with three terms?
Yes — find the GCD of all three numbers and divide each by it. For 12 : 18 : 30, the GCD is 6, giving 2 : 3 : 5.
Is simplifying a ratio the same as reducing a fraction?
Essentially yes. A ratio A : B behaves like the fraction A/B, and both are reduced by dividing by the GCD of the two terms.