Multiplying fractions
Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5)
What a learner can do afterwards
- Calculate 4 × 3/8 using repeated addition or the rule n × a/b = (n×a)/b
- Multiply 2 1/3 × 3 and express as a mixed number
- Use a visual model to show why 5 × 1/4 = 5/4
The lesson
You already know that a fraction like 3/8 means 3 equal parts out of 8. Multiplying a fraction by a whole number is just adding that same fraction to itself, again and again.
Ivy shares pizza with 3 friends. Each friend gets 2 1/3 slices. How many slices in total? First change 2 1/3 to a single fraction: 7/3. Then multiply: 3 × 7/3 = 21/3 = 7. Ivy needs 7 slices in total.
The bottom number of the fraction never changes when you multiply by a whole number. Only the top number grows, because you are counting more equal parts.
To multiply a fraction by a whole number, multiply the top number and keep the bottom number the same. Change mixed numbers into a single fraction first.
Watch it
Where it sits
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.