Example 1: Two proper fractions
Calculate 2/3 × 3/5.
- 1Multiply the numerators: 2 × 3 = 6.
- 2Multiply the denominators: 3 × 5 = 15.
- 3This gives 6/15.
- 4Simplify by dividing both by 3: 2/5.
Answer: 2/5
Arithmetic · Grades 5–7
Multiplying Fractions: Method, Examples and Printable Test
Multiplying fractions is the easiest of the four fraction operations: multiply the tops, multiply the bottoms, simplify. The difficulty is not the method but unlearning the common denominator habit that adding fractions builds.
Multiplying Fractions formula
a/b × c/d = (a × c) / (b × d)
Multiply the numerators to get the new numerator and the denominators to get the new denominator. No common denominator is needed. Simplifying before multiplying, by cancelling any factor shared between a numerator and a denominator, keeps the numbers small.
- a, c
- The numerators, or top numbers
- b, d
- The denominators, or bottom numbers
- ×
- Read as 'of' — 1/2 × 3/4 is one half of three quarters
- Simplify
- Divide top and bottom by any common factor
Worked examples
Example 2: Cancelling first
Calculate 4/9 × 3/8.
- 1The 4 and the 8 share a factor of 4: they become 1 and 2.
- 2The 3 and the 9 share a factor of 3: they become 1 and 3.
- 3Now multiply the simplified fractions: 1/3 × 1/2.
- 4This gives 1/6, already in lowest terms.
Answer: 1/6
Example 3: A mixed number
Calculate 1½ × 2/3.
- 1Convert the mixed number to an improper fraction: 1½ = 3/2.
- 2Multiply: (3 × 2) / (2 × 3) = 6/6.
- 3Simplify: 6/6 = 1.
Answer: 1
Multiplying Fractions practice questions with answers
Work through these in order. Each answer opens to show the full method, so you can check your reasoning rather than just your final number.
- Question 1easy
Calculate: 1/2 × 3/4
Show answer and worked solution
Answer: 3/8
Multiply tops and bottoms: (1×3)/(2×4) = 3/8.
- Question 2easy
Calculate: 2/5 × 1/3
Show answer and worked solution
Answer: 2/15
(2×1)/(5×3) = 2/15.
- Question 3easy
Calculate: 3/4 × 4
Show answer and worked solution
Answer: 3
Write 4 as 4/1: (3×4)/(4×1) = 12/4 = 3.
- Question 4easy
Calculate: 1/3 × 1/3
Show answer and worked solution
Answer: 1/9
(1×1)/(3×3) = 1/9.
- Question 5medium
Calculate: 2/3 × 9/10
Show answer and worked solution
Answer: 3/5
(2×9)/(3×10) = 18/30, which simplifies by 6 to 3/5.
- Question 6medium
Calculate: 5/6 × 3/10
Show answer and worked solution
Answer: 1/4
Cancel 5 with 10 and 3 with 6: 1/2 × 1/2 = 1/4.
- Question 7medium
What is 3/4 of 20?
Show answer and worked solution
Answer: 15
'Of' means multiply: 3/4 × 20 = 60/4 = 15.
- Question 8hard
Calculate: 2¼ × 2/3
Show answer and worked solution
Answer: 3/2 or 1½
2¼ = 9/4. Then (9×2)/(4×3) = 18/12, which simplifies to 3/2.
- Question 9hard
A recipe needs 3/4 cup of flour. How much for 2/3 of a batch?
Show answer and worked solution
Answer: 1/2 cup
3/4 × 2/3 = 6/12 = 1/2 cup.
- Question 10hard
Calculate: 1/2 × 2/3 × 3/4
Show answer and worked solution
Answer: 1/4
Multiply across: 6/24, which simplifies to 1/4. Cancelling first is faster.
Turn this into a printable test
Generate a multiplying fractions test at the grade and difficulty you need, with a complete worked answer key and equivalent versions for retakes.
Prefer free practice first? free fraction worksheets with answers
Why multiplying can make numbers smaller
Every student arrives with the belief that multiplication increases and division decreases, and fractions break both halves of it. Multiplying by 1/2 halves a number. This is not a special rule to memorise; it follows from reading the multiplication sign as the word 'of'. One half of three quarters is obviously smaller than three quarters, and once students hear the sentence that way the surprise disappears.
The same reading makes word problems tractable. Two thirds of a batch, three quarters of a class, half of a remaining amount are all multiplications, and students who translate 'of' into × solve them without needing to identify a problem type.
Cancel before you multiply
Multiplying 4/9 × 3/8 straight across gives 12/72, which then has to be simplified by 12. Cancelling first turns the same question into 1/3 × 1/2 and the arithmetic becomes trivial. The two routes give the same answer, but the second produces far fewer errors because the numbers stay small.
The rule is that any numerator can cancel with any denominator, not just the one directly beneath it. Students who understand this handle three-fraction products comfortably; students who do not end up multiplying large numbers and then struggling to simplify them.
Common mistakes with multiplying fractions
✗ Finding a common denominator before multiplying.
✓ Common denominators are only needed for addition and subtraction. Multiply straight across instead.
✗ Multiplying a mixed number without converting it first.
✓ Convert to an improper fraction. Multiplying the whole parts and fractions separately gives the wrong answer.
✗ Expecting the product to be larger than both fractions.
✓ Multiplying by a fraction less than 1 makes a number smaller. Half of three quarters is less than three quarters.
✗ Leaving the answer unsimplified.
✓ Divide the numerator and denominator by any common factor. Cancelling before multiplying avoids large numbers entirely.
Multiplying Fractions FAQ
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. For example, 2/3 × 3/5 = 6/15 = 2/5.
Do you need a common denominator to multiply fractions?
No. Common denominators are only required for addition and subtraction. Multiplication works straight across.
How do you multiply a fraction by a whole number?
Write the whole number over 1 and multiply as normal. For example, 3/4 × 4 becomes 3/4 × 4/1 = 12/4 = 3.
How do you multiply mixed numbers?
Convert each mixed number to an improper fraction first, then multiply the numerators and denominators and simplify.
Why does multiplying make the answer smaller?
Multiplying by a fraction less than 1 takes a part of the number. One half of three quarters is 3/8, which is smaller than 3/4.