Multiply 3/4 × 2/9.
Give me a hint
Look for common factors across the product before multiplying.
Compare a worked response
1/6
6/36 simplifies to 1/6. You can simplify 3 with 9 and 2 with 4 first.
Multiply fractions & mixed numbers
A fraction of an amount can be smaller than the amount. Use an area model to explain the product.
Your learning goal
Multiply positive fractions, mixed numbers and whole numbers, and justify the result with a model.
Understand the idea
Whole-number multiplication counts groups
Three groups of 2/3 is 3 × 2/3 = 6/3 = 2. The denominator stays 3 when counting repeated thirds. Writing the whole number as 3/1 makes the general multiplication rule visible.
Words worth knowing
- Factor
- A number being multiplied.
- Product
- The result of multiplication.
- Area model
- A diagram that represents multiplication using overlapping parts of a rectangle.
- Common-factor simplification
- Dividing a numerator and a denominator by the same factor within a product.
Make it visible
Find the overlap—and explain its unit.
Predict a result, change a value, and use the diagram to explain your reasoning.
Every outlined unit rectangle represents one whole. Dots identify the overlap; the controls support fractions and mixed amounts up to two wholes.
Fraction multiplication takes a part of a part
For 2/3 × 3/4, shade 2/3 of the width and 3/4 of the height of one rectangle. The overlap contains 6 of 12 equal small rectangles, so the product is 6/12 = 1/2 of the original whole.
Multiply numerators and denominators
The new unit parts come from both partitions: thirds by fourths make twelfths. Thus (a/b) × (c/d) = (a × c)/(b × d), with non-zero denominators. You do not need a common denominator first. Convert mixed numbers to improper fractions before using this rule.
Khan AcademyWatch · pause · explain
Multiplying fractions with an area model
Pause before the next step. Explain what the shaded region or group represents, then compare it with the model above.
Open on YouTube →The player loads when you choose to watch. Captions and availability depend on the provider.Simplify factors and predict the effect
In 4/9 × 3/8, divide 4 and 8 by 4, and 3 and 9 by 3, before multiplying: 1/3 × 1/2 = 1/6. This works because the entire numerator and denominator form one product. For a positive amount, multiplying by a number between 0 and 1 makes it smaller; multiplying by a number greater than 1 makes it larger.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
Find 2/5 of 3/4 of a sheet
- Interpret “of” as multiplication: 2/5 × 3/4.
- A five-by-four partition contains 20 equal regions; the overlap contains 6.
- 6/20 = 3/10 of the original sheet. This is less than 3/4 because only part of that amount is kept.
Multiply 1 1/2 × 2 2/3
- Convert: 1 1/2 = 3/2 and 2 2/3 = 8/3.
- Multiply and simplify: (3 × 8)/(2 × 3) = 8/2 = 4.
- Check the size: one and a half groups of 2 2/3 is 2 2/3 + 1 1/3 = 4.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Find 3/5 of 20 litres.
Give me a hint
First find one fifth of 20, then count three fifths.
Compare a worked response
12 litres
20 ÷ 5 = 4 litres; 3 × 4 = 12 litres.
Independent practice
Build a strategy you can explain.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Check the concepts, too.
What does the answer mean?
Scaling a recipe by 3/4 means multiplying every ingredient by 3/4. Changing only one ingredient does not preserve the recipe.