Fractions and percentages of amounts
Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)
What a learner can do afterwards
- Calculate a fraction of a given amount by multiplying
- Calculate a percentage of a given amount by converting to a decimal and multiplying
- Use the operator interpretation to solve multi-step problems involving discounts, taxes, and portions
1 · Read
In maths, the word 'of' is a hidden multiply sign. When you read '3/4 of 200', it means 3/4 × 200. Once you spot 'of' next to a fraction or a percentage, you know exactly what to do: multiply.
Find 3/4 of 200. First divide by the bottom number: 200 ÷ 4 = 50. That is one part. Then multiply by the top number: 50 × 3 = 150. So 3/4 of 200 is 150.
Percentages work the same way. 'Percent' means 'out of 100', so change the percentage to a decimal by dividing by 100, then multiply. For 20% of 50: 20 ÷ 100 = 0.20, and 0.20 × 50 = 10.
For a discount or tax problem, find the percentage of the amount first. That first answer is not the final answer - subtract it from (or add it to) the original amount to finish the job.
See 'of' with a fraction or percentage? Turn it into a multiply, find the piece, then finish the problem.
2 · Watch
Take it off screen
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.