Understanding the ratio
A ratio compares two quantities. In part-to-part ratios, you compare one part of a whole to another part. In part-to-whole ratios, you compare one part to the total amount.
Method
- Read the ratio carefully. Decide whether the question asks for part-to-part or part-to-whole.
- Match the order of the quantities. If the ratio is written as A:B, keep A first and B second.
- Simplify if possible. Divide both numbers by their greatest common factor.
- For part-to-whole, add the parts. If the ratio is given as several parts, the whole is the sum of those parts.
- Use exact values. If the exercise asks for a missing quantity, set up the ratio with equivalent parts and solve by multiplication or division.
Check your answer
- For a simplified ratio, the numbers should have no common factor greater than 1.
- For part-to-whole, the part should be smaller than the whole, and the whole should equal the sum of all parts in the ratio.
- Re-read the question to make sure the ratio matches what is being asked.
Example check idea
If a ratio of two parts is 3:5, the total number of equal parts is 8, so a part-to-whole ratio involving the first part would be 3:8.