Fractions of amounts (harder)
Solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number
What a learner can do afterwards
- Find 3/5 of 20
- Calculate 2/3 of 18 and explain the two-step process (divide then multiply)
- Solve: A bag has 24 sweets, 3/8 are red. How many red sweets?
1 · Read
You already know how to find a unit fraction of a number, like 1/4 of something: you just divide. Now you are ready for fractions like 2/3 or 3/5, where the top number is more than 1. There is a simple two-step trick: first divide by the bottom number, then multiply by the top number.
Step 1: divide 18 by 3, the bottom number. 18 divided by 3 is 6. Step 2: multiply that answer by 2, the top number. 6 times 2 is 12. So 2/3 of 18 is 12.
Always divide first, then multiply. If you multiply by the top number first, the numbers get big and harder to work with. Dividing first keeps things small and friendly.
To find a fraction of an amount, divide by the bottom number, then multiply by the top number.
More to read
Create and solve one-step word problems involving fractions
Word problems with fractions are like little stories that hide a math question.
Read the story and find two things: the whole amount, and the fraction of it the question asks about. For example: A farmer picks 24 apples and puts 3/8 of them in a basket. How many apples go in the basket?
The whole amount is 24. The fraction is 3/8. Now do two steps.
Step one: divide the whole by the bottom number. 24 divided by 8 is 3. That is one eighth of the apples.
Step two: multiply by the top number. 3 times 3 is 9. So 9 apples go in the basket.
Try another one. A team has 30 players and 2/5 of them are new. 30 divided by 5 is 6, and 2 times 6 is 12, so 12 players are new.
The two steps always work. Divide first, multiply second, and check that your answer is smaller than the whole. A fraction of an amount can never be bigger than the amount itself.
Identify and represent a whole as two parts - a unit fraction and a non-unit fraction
A fraction has a top number and a bottom number. The bottom number tells you how many equal parts the whole is split into. The top number tells you how many of those parts you are talking about.
When the top number is 1, the fraction is called a unit fraction. 1/5 means one part out of five. 1/3 means one part out of three.
When the top number is bigger than 1, it is a non-unit fraction. 3/5 means three parts out of five. You can think of it as three copies of 1/5.
This is why finding 3/5 of 20 works in two steps. First find one fifth of 20, which is 20 split into 5 equal parts, giving 4. That is the unit fraction part. Then take three of those fifths: 3 times 4 is 12.
Every non-unit fraction is just a bunch of unit fractions added together. 4/7 of a chocolate bar is the same as 1/7 plus 1/7 plus 1/7 plus 1/7. Once you can find one part, you can find any number of parts.
2 · Watch
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Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
15 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.