Quick answer: 12 : 18 simplifies to 2 : 3 by dividing both terms by their GCF, 6; and 3 : 4 = 9 : x gives x = 4 × 9 ÷ 3 = 12.
How it's calculated
Simplify: divide every term by the greatest common factor of all the terms. If a term has decimals, first multiply all the terms by 10, 100 … so they are whole: 2.5 : 1.5 → 25 : 15 → 5 : 3.
Solve a proportion: in a : b = c : x the cross products are equal, a × x = b × c, so x = b × c ÷ a.
Share a total: add the parts of the ratio, divide the total by that sum to get one part, then multiply by each term. Sharing 1,200 in 2 : 3 : 5 gives one part = 120 and shares 240, 360 and 600.
A ratio of two numbers is also a fraction and a percentage: 2 : 3 means the first is 2/3 of the second; see the fraction calculator and percentage calculator.
Worked examples
- Simplify 12 : 18: GCF 6 → 2 : 3
- Solve 3 : 4 = 9 : x: x = 4 × 9 ÷ 3 = 12
- Share 1,200 in 2 : 3 : 5: 1,200 ÷ 10 = 120 → 240 : 360 : 600
Frequently asked questions
Does the order of a ratio matter?
Yes. 2 : 3 and 3 : 2 are different; keep the terms in the order the question gives them.
How do I scale a recipe with a ratio?
Use the proportion mode: if 3 cups of flour need 4 eggs, then 9 cups need x eggs, and x = 4 × 9 ÷ 3 = 12.
Can a ratio have more than two terms?
Yes. Simplify and share both accept up to 10 terms, such as 2 : 3 : 5.
How do I simplify 12 : 18?
Divide both sides by 6 and you get 2 : 3.
How do I split money in a ratio?
Add the parts, divide the total by that number, then multiply back. Sharing 1,200 riyals as 2 : 3 : 5 means ten parts of 120, so 240, 360 and 600.
What does a 16:9 screen mean?
Every 16 units of width come with 9 of height, so a screen 160 cm wide is 90 cm tall.