Multiplying fractions (age 10+)
Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form
What a learner can do afterwards
- Compute (2/3) × (4/5) = 8/15 and show with an area model
- Use a visual model to demonstrate (2/3) × 4 = 8/3 = 2 2/3
- Simplify the product 3/4 × 2/3 = 6/12 = 1/2
1 · Read
You already know how to multiply fractions and simplify them. Now you will multiply two proper fractions, like 2/3 times 4/5. Think of (a/b) times q as this: split q into b equal parts, then take a of those parts.
Multiply 3/4 x 2/3. Multiply the tops: 3 x 2 = 6. Multiply the bottoms: 4 x 3 = 12. That gives 6/12. Now simplify: divide top and bottom by 6, and you get 1/2.
A whole number works the same way. For 2/3 x 4, write 4 as 4/1, then multiply straight across: 2 x 4 = 8 and 3 x 1 = 3, so you get 8/3, which is 2 and 2/3.
Multiply the tops, multiply the bottoms, then simplify if you can.
More to read
Multiply fractions: FAQ
How can we picture multiplying a fraction by a whole number? There are many ways. We can use area models, groups of objects, tape diagrams, or number lines. Each one helps us see what the multiplication is really doing.
For example, to show (4/5) x 10 on a number line, draw a line from 0 to 10 and split it into 5 equal parts. Each part is 2 units long, because 10 divided by 5 is 2. Then count 4 of those parts: 2 + 2 + 2 + 2 = 8. So (4/5) x 10 = 8.
The big idea is that (a/b) x q means: split q into b equal parts, then take a of those parts. The denominator tells you how many parts to make, and the numerator tells you how many parts to take.
When you multiply two fractions, the same idea works. Split the first fraction into parts using the second fraction's denominator, then keep the parts the numerator asks for. An area model shows this nicely: shade 2/3 of a rectangle one way, 4/5 the other way, and the overlap is the product, 8/15.
After you multiply, always check if your answer can be written in simplest form by dividing the top and bottom by the same number.
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2 · Watch
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Where it sits
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Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 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.