Multiplying Fractions Calculator
Type two fractions or mixed numbers to multiply them, with common factors cancelled first so the numbers stay small.
4/9 × 3/8 =
1/6
4/9 × 3/8 = 1/6, about 0.1667 as a decimal.
- As a decimal
- ≈ 0.166667
- Repeating
- 0.1(6)
How to multiply fractions
Multiply the numerators together and the denominators together; no common denominator is needed. 2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15. Multiplying by a fraction takes that fraction of the number, so 1/2 × 3/4 is “half of three quarters”, which is 3/8.
Cancel before you multiply to keep the numbers small. In 4/9 × 3/8, the 4 and the 8 share a factor of 4, and the 3 and the 9 share 3, so the sum becomes 1/3 × 1/2 = 1/6. Multiplying first gives 12/72, which simplifies to the same 1/6 with more work.
Turn mixed numbers into improper fractions before multiplying: 2 1/2 × 1 1/3 = 5/2 × 4/3 = 20/6 = 3 1/3. Multiplying the whole parts and the fraction parts separately gives the wrong answer (2 × 1 + 1/2 × 1/3 = 2 1/6).
a/b × c/d = (a × c) / (b × d)
- Grade 5 standards define a fraction times a number as taking parts of a whole: (a/b) × q means a parts of a partition of q into b equal parts (5.NF.B.4). Source: Common Core State Standards, Grade 5 Number and Operations: Fractions.
Fraction products
Products with the factors cancelled across the fractions before multiplying, and the decimal value.
| Product | After cancelling | Answer | Decimal |
|---|---|---|---|
| 1/2 × 1/2 | 1/2 × 1/2 | 1/4 | 0.25 |
| 1/2 × 3/4 | 1/2 × 3/4 | 3/8 | 0.375 |
| 2/3 × 3/4 | 1/1 × 1/2 | 1/2 | 0.5 |
| 4/9 × 3/8 | 1/3 × 1/2 | 1/6 | 0.1667 |
| 3/5 × 5/6 | 1/1 × 1/2 | 1/2 | 0.5 |
| 5/8 × 4/15 | 1/2 × 1/3 | 1/6 | 0.1667 |
| 7/10 × 5/14 | 1/2 × 1/2 | 1/4 | 0.25 |
| 2/3 × 9 | 2/1 × 3/1 | 6 | 6 |
| 3/4 × 12 | 3/1 × 3/1 | 9 | 9 |
| 1 1/2 × 2/3 | 1/1 × 1/1 | 1 | 1 |
Show all 14 rowsShow fewer
| 2 1/2 × 1 1/3 | 5/1 × 2/3 | 3 1/3 | 3.3333 |
| 3 3/4 × 2 2/5 | 3/1 × 3/1 | 9 | 9 |
| −2/3 × 3/7 | −2/1 × 1/7 | −2/7 | −0.2857 |
| 6/25 × 10/9 | 2/5 × 2/3 | 4/15 | 0.2667 |
Frequently Asked Questions
Why does multiplying by a fraction make a number smaller?
Multiplying by a fraction less than 1 takes only part of the number: 3/4 of 20 is 15. Multiplying by an improper fraction such as 3/2 makes it bigger, because that is more than one whole.
How do I multiply a fraction by a whole number?
Write the whole number over 1 and multiply as usual: 2/3 × 9 = 2/3 × 9/1 = 18/3 = 6. Cancelling the 3 into the 9 first gives 2 × 3 = 6 directly.
Can I cancel any numerator with any denominator?
In a product, yes: any numerator with any denominator, even across the two fractions, because multiplication can be done in any order. You cannot cancel like this when adding or subtracting.