Percentage

What is a percentage?

A percentage is a way of expressing a number as a fraction of 100. To turn a score of $a$ out of $b$ into a percentage, compute $$\dfrac{a}{b} \times 100$$When combining scores from more than one test, add up all the marks scored and all the marks available first, and only then convert the totals to a percentage. Converting each test to a percentage and averaging those percentages gives a different (and usually wrong) answer whenever the tests are out of different totals.

Worked example

A girl scored 60 out of 75 in English, 60 out of 90 in Mathematics, and 80 out of 100 in Science. Find her combined score as a percentage across all three subjects.

Solution: Add up the marks scored: $60 + 60 + 80 = 200$. Add up the marks available: $75 + 90 + 100 = 265$. The combined percentage is