What is a ratio
A ratio compares two or more quantities, showing how many times one fits into the other. It's written with a colon, like 2:3, and read as "2 to 3". Unlike a fraction, a ratio can compare more than two quantities at once, like 2:3:5.
How to simplify a ratio
Simplifying a ratio works like simplifying a fraction: divide every term by the greatest common divisor (GCD) between them. The ratio 8:12, for example, simplifies to 2:3, because the GCD of 8 and 12 is 4, and 8÷4=2, 12÷4=3. This calculator uses the Euclidean algorithm to find the GCD, and it also works for ratios with three or more terms.
How to split a value by a ratio
To split a total value according to a ratio, add up all the parts of the ratio to find the total number of shares, then give each part the matching fraction of the total value. Splitting 100 by the ratio 2:3:5, for example, gives 20, 30, and 50: the parts add up to 10, and each one gets 2/10, 3/10, and 5/10 of 100, respectively.
Practical example
Three partners invested in a business in the 2:3:5 proportion and will split a $10,000 profit according to that ratio. Adding up the parts (2+3+5=10), each partner gets $2,000, $3,000, and $5,000, respectively.