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.
More to read
Key ideas: Multiply fractions by unit fractions by making simpler problems
Have you met a unit fraction? It is a fraction with 1 on top, like 1/2, 1/5, or 1/7. Multiplying by a unit fraction means finding one part of a number. Think of 1/5 × 35 as saying one fifth of 35. Split 35 into 5 equal groups and each group is 7, so 1/5 × 35 = 7.
Once you know 1/5 × 35 = 7, harder questions get easy. 2/5 × 35 just means two of those fifths, so 2 × 7 = 14. And 3/5 × 35 = 3 × 7 = 21.
So when you see a fraction times a whole number, find one part first, then multiply by the top number. The word of is your clue that multiplying is the tool to grab.
Understanding fraction word problems with multiplication and division
Fraction word problems can look like twins, but the questions are secretly different. You do not pick add or multiply by staring at the numbers. You ask what the problem wants you to find.
Estaban has 3/4 of a liter of water. He drinks 1/2 of his water. How much did he drink? He drank half OF his three quarters, and of means multiply. So 1/2 × 3/4: 1 times 3 is 3, and 2 times 4 is 8, which is 3/8 of a liter.
Try this one. Zane has 5/6 of a pizza and gives 1/3 of it to a friend. That is 1/3 of 5/6, so 1/3 × 5/6 = 5/18 of the pizza.
When a problem says part of a part, multiply. When it asks how many equal pieces fit, think division. Asking the right question first keeps you safe.
How to Divide and Multiply Fractions: 5 Steps
Multiplying fractions is one of the friendliest jobs in math.
1. Line up the fractions side by side. 2. Multiply the top numbers, called the numerators. Write that on top. 3. Multiply the bottom numbers, called the denominators. Write that on the bottom. 4. Simplify the answer by dividing the top and bottom by the same number until nothing divides both.
Example: 2/3 × 4/5. Tops: 2 × 4 = 8. Bottoms: 3 × 5 = 15. The answer is 8/15, and it is already simple.
One more example with simplifying: 3/4 × 2/9 = 6/36. Both 6 and 36 divide by 6, so the real answer is 1/6.
No common denominators needed, no borrowing. Just top times top, bottom times bottom, then simplify.
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2 · Watch
En anglaisTake 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.
18 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.