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Simplify ratios, convert to fractions and percentages, and scale ratios to a given value.
Ratio Formulas:
Simplify a:b by dividing both by GCD(a,b)
Ratio to fraction: a:(a+b)
Ratio to percent: a/(a+b) x 100 : b/(a+b) x 100
Scale: multiply both parts by the scale factor
A ratio compares two or more quantities. A ratio of 3:4 means for every 3 of the first quantity, there are 4 of the second. Ratios can be simplified just like fractions.
Divide both parts by their Greatest Common Divisor (GCD). For example, 12:18 simplifies to 2:3 because GCD(12,18) = 6.
Divide each part by the total (sum of parts) and multiply by 100. For ratio 1:3, the total is 4, so 1/4 = 25% and 3/4 = 75%.
A proportion states that two ratios are equal: a/b = c/d. If you know three of the four values, you can solve for the fourth by cross-multiplying.
A unit ratio has 1 as one of its parts. For example, 3:12 simplifies to 1:4, which means for every 1 of the first quantity there are 4 of the second.