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
The lesson
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.
Watch it
Where it sits
Learn first
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.