Direct answer

A ratio compares two quantities. Simplify by dividing both sides by their greatest common divisor (GCD). Find a missing value with cross-multiplication: if a : b = x : d, then x = (a × d) ÷ b.

Ratio formulas

A ratio a : b compares two quantities and can also be written as the fraction a/b. The tools above use these formulas:

• Simplify: (a ÷ GCD) : (b ÷ GCD), where GCD is the greatest common divisor of a and b.
• Missing value: if a : b = x : d, then x = (a × d) ÷ b.
• Scale: (a × k) : (b × k), where k is the scale factor.
• Share of the total: in a : b, the first part is a/(a + b) of the whole and the second is b/(a + b). As percentages: a/(a + b) × 100 and b/(a + b) × 100.

Worked examples

Example 1 (simplify): 12 : 18. GCD of 12 and 18 is 6. 12 ÷ 6 = 2, 18 ÷ 6 = 3. Simplified ratio = 2 : 3.

Example 2 (missing value): 3 : 5 = x : 25. x = (3 × 25) ÷ 5 = 15. So 3 : 5 = 15 : 25.

Example 3 (scale): Scale 2 : 3 by 4: multiply both sides by 4 → 8 : 12.

Example 4 (scale): Scale 5 : 7 by 3: multiply both sides by 3 → 15 : 21.

Try it above with the Scale tool: enter the two sides of the ratio and the scale factor to get the scaled ratio with steps.

What to watch out for

Order matters: 2 : 3 is not the same as 3 : 2. Keep the quantities in the same order on both sides of the ratio.

FAQs

How do you simplify a ratio?

Divide both numbers by their greatest common divisor (GCD). For example, the GCD of 12 and 18 is 6, so 12 : 18 simplifies to 2 : 3. The simplified ratio keeps the same relationship in the smallest whole numbers.

How do you find a missing value in a ratio?

Cross-multiply: if a : b = x : d, then x = (a × d) ÷ b. For example, in 3 : 5 = x : 25, x = (3 × 25) ÷ 5 = 15. Always keep the quantities in the same order on both sides.

What is the difference between a ratio and a fraction?

A ratio compares two quantities (2 : 3); a fraction is one quantity divided by another (2/3). A part-to-part ratio 2 : 3 means 2 parts out of 5 total, which equals the fraction 2/5 of the whole.

How do you scale a ratio up?

Multiply both sides by the same number, e.g. 2 : 3 scaled by 4 is 8 : 12. Scaling keeps the relationship identical while changing the size of the quantities. Use it to enlarge recipes, maps, or models without distorting proportions.

How do you split an amount in a given ratio?

Add the parts of the ratio to find the total number of shares, then divide the amount by that total to get the value of one share. Multiply one share by each part of the ratio to get each portion. For example, splitting $120 in the ratio 3 : 5 gives 8 shares of $15, so the portions are $45 and $75.

How do you convert a ratio to a percentage?

Divide each part by the total of all parts and multiply by 100. For the ratio 2 : 3, the total is 5, so the parts are 2/5 = 40% and 3/5 = 60%. This is useful when you want to show each share as a portion of the whole.

Related calculators: Fraction Calculator · Percentage Calculator · Grade Calculator

Last updated: November 1, 2026.