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Percentages

Interpret a percentage as a fraction of a stated base. Calculate a percentage amount and a percentage change without confusing the original and final values.

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What you’ll learn

Convert a percentage to a fraction or decimal.
Calculate a part from a percentage and its base.
Use the original value as the base for percentage change.

Identify what counts as one hundred percent

A percentage describes a part relative to a base. In “20% of 80,” the base is 80 and the percentage is 20/100. Naming the base first prevents many errors.

Separate the change from the final amount

For an increase, calculate the change and add it to the original value. For percentage change between two values, divide the change by the original value before multiplying by 100.

A mistake to avoid

Increasing and decreasing by the same percentage do not usually undo each other because the second percentage uses a different base. Also distinguish percentage points from relative percentage change.

Worked example

Increase 80 by 20%

20% of 80 is 0.20 × 80 = 16. The new value is 80 + 16 = 96. The change as a percentage of the original value is 16 ÷ 80 × 100 = 20%, not 16 ÷ 96 × 100.

Learning paths that include this skill

Choose the route that fits your goal. The same skill can be useful in more than one subject or stage of learning.

Preparing for algebraPre-algebraConnect arithmetic to algebra through signed numbers, fractions, proportions, equations, and graphs. Review the specific foundation that blocks the next step.Signed numbers · Equivalent fractions · Decimals · Proportions · +6 more Goal-led refresherAdult math refresherRefresh the mathematics behind a real task, from a percentage or measurement to an equation or graph. Use familiar goals and revisit only the skills you need.Place value · Addition & subtraction · Multiplication · Long division · +12 more Investing concept foundationsInvesting foundationsBuild the vocabulary and numerical understanding needed to read an investing explanation carefully. The sequence teaches concepts through hypothetical examples, without choosing investments or allocations.Saving and investing · Decimals · Percentages · Reading data · +4 more

Reading dataRead a table or chart in context and summarize a small data set. Distinguish mean, median, and range instead of expecting one number to tell the whole story.ProbabilityDefine an event and the possible outcomes before calculating its probability. Use fractions to describe chance and check whether successive events are independent.Graphs & coordinatesRead a graph as a relationship between quantities. Check axes and scale, connect points to an equation, and interpret the change between two points.

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