Quick brief
What to know before you calculate
A short read on the assumptions, trade-offs and definitions that shape the answer.
- Fractions, ratios and percentages can describe the same relationship.
- The base value decides what a percentage actually means.
- Converting the format can make a difficult comparison easier.
Three ways to describe part of a whole
A fraction such as 3/10, a ratio such as 3 to 7 and a percentage such as 30 percent can all describe related ideas. The format changes depending on the question. Fractions are useful for exact arithmetic, ratios are useful for mixing or sharing, and percentages are useful for comparing against 100.
Keep the base visible
A percentage is always relative to something. Thirty percent of 200 is not the same as 30 percent of 80. Many mistakes happen when the base changes without being noticed. When in doubt, write down the starting value, the change and the final value before calculating.
Simplify before comparing
Fractions and ratios are often easier to compare after simplification. A ratio of 12 to 18 becomes 2 to 3. A fraction of 20/50 becomes 2/5. Once simplified, converting to a percentage can make the result easier to communicate.
Use the format that answers the question
For recipe scaling, a ratio may be clearest. For a discount, a percentage is usually best. For exact maths homework, a simplified fraction may be required. The underlying relationship is the same, but the most useful format depends on what someone needs to do next.
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