Percentages as fractions
Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%
What a learner can do afterwards
- Convert fluently between percentages, fractions, and decimals
- Express one quantity as a percentage of another
- Calculate percentage increases and decreases and interpret percentages greater than 100%
1 · Read
Percent means per hundred. A percentage compares an amount with a stated whole or starting amount. That reference amount is 100%. Keep track of which amount is the whole before converting, comparing or calculating a change.
To change a percentage to a fraction, write its number over 100. Simplify by dividing numerator and denominator by the same common factor. For 18%, write 18/100 and divide both by 2 to get 9/50. To change a percentage to a decimal, divide by 100: 18% = 0.18. These methods also work above 100%.
To change a fraction to a percentage, make equivalent hundredths or divide its numerator by its denominator and multiply by 100. For 11/20, multiply both numbers by 5: 55/100 = 0.55 = 55%. To change any decimal to a percentage, multiply by 100 to find the number before the % sign. Small decimals can give percentages below 1%: 0.0015 × 100 = 0.15, so 0.0015 = 0.15%.
To express one quantity as a percentage of a whole, write part/whole. Simplify first if helpful, then make hundredths or divide and multiply by 100. If 13 of 50 tickets are used, 13/50 = 26/100 = 26%. The denominator is the total number of tickets, not the unused tickets.
Percentages may be greater than 100%. They compare with the starting whole, rather than describing only parts inside it. For a positive starting amount, anything above 100% is more than that starting amount. For a starting amount of zero, multiplying by any percentage still gives zero.
To calculate an amount above 100%, keep the full starting amount and add the extra percentage. For 140% of £50, keep £50 and add 40%: four 10% parts of £5 make £20. The result is £70. Useful extra parts include 20% as one fifth and 25% as one quarter. Divide the starting amount by 5 or 4 to find them.
For percentage change, first find the increase or decrease. Divide that change by the positive original amount, then multiply by 100 to find the number before the % sign. The original is the reference whole. From £90 to £99, the increase is £9, so 9/90 × 100 = 10, giving a 10% increase. From £90 to £81, the decrease is also £9, giving a 10% decrease. Name the direction as well as the percentage.
A percentage is a fraction out of 100, and the same amount can be written as a fraction, a decimal, or a percentage.
Questions written for this learning dataset. Linked fraction, decimal and percentage videos by Khan Academy.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
20 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.