Multiplying fractions
I can multiply two fractions and explain the product as a fraction of a fraction using an area model.
Learn
Half of a garden is vegetables, and 3/4 of the vegetable part is tomatoes. What fraction of the garden is tomatoes?
1/2 × 3/4 means “1/2 of 3/4”. On a square, shade 3/4 one way and 1/2 the other way. The overlap is the product.
The square is cut into 2 × 4 = 8 equal cells and 1 × 3 = 3 overlap. So 1/2 × 3/4 = 3/8.
Rule: multiply the numerators and multiply the denominators. You do not need a common denominator.
When both fractions are less than 1, the product is smaller than each of them. Simplify the result when you can.
Worked examples
1/2 × 3/4
- Shade 3 of 4 columns.
- Shade 1 of 2 rows.
- 3 of 8 cells overlap: 3/8.
2/3 × 3/5
- Numerators: 2 × 3 = 6.
- Denominators: 3 × 5 = 15.
- 6/15 = 2/5.
Explore
Change both fractions. Count the overlapping cells and the total cells — compare with numerator × numerator and denominator × denominator.
Columns fraction
Rows fraction
Numerators are kept at or below their denominators in this model.
Guided practice
Use the hints as much as you like. You can try each question as many times as you need.
0 of 2 solved
What product does the area model show?
1/2 × 3/4 = ?
Independent practice
Answers are checked exactly — equivalent fractions count unless a question asks for a particular form.
0 of 4 solved
2/3 × 3/5 in simplest form.
3/4 × 2/3 in simplest form.
Half the garden is vegetables; 3/4 of that is tomatoes. What fraction of the garden is tomatoes?
Is 4/5 × 2/3 bigger or smaller than 2/3?
Common mistakes
Finding a common denominator before multiplying.
Why it happens: It is not wrong, but it is unnecessary and leads to big numbers.
What to do: Multiply straight across, then simplify.
Expecting the product to be bigger than both fractions.
Why it happens: Taking a part of a part gives a smaller piece.
What to do: Check with the area model: the overlap is inside both shaded regions.
Lesson check
Three practice questions to check your understanding. Hints and retries are allowed, so this counts as practice — not mastery.
0 of 3 solved
1/3 × 1/4 = ?
5/6 × 3/5 in simplest form.
3/2 × 4/9 in simplest form.
Show mastery on your own
Ready? Answer 4 new questions with no hints and one try each. This is the only way a lesson is marked as mastered.
Start mastery check