Choose the reference amount for a percentage

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Choose the reference amount for a percentage

A percentage means a fraction out of one hundred. To express A as a percentage of B, calculate 100A/B with nonzero B as the stated reference. Swapping the reference changes the question and usually changes the answer.

A percentage can exceed 100 when the compared quantity is greater than the reference. If 150 is compared with 100, it is 150% of the reference, but the increase is 50%. The final proportion and the change proportion are distinct.

For the conventional percentage change from a positive original amount, divide the signed change by the original amount. A decrease can be described by a negative signed change or a positive decrease percentage, provided the wording is clear.

Worked example: A value increases from 80 to 100. Find the percentage increase.

The increase is 20.

Use the original 80 as reference.

Calculate (20/80) × 100.

Answer: 25%.

Check your understanding: What percentage of 80 is 100?

Answer: 125%.

Why: This compares the final value itself with the original.