Key takeaways
- a/b × c/d = (a×c) / (b×d).
- No common denominator is needed — just multiply straight across.
- Multiplying two fractions smaller than 1 always makes the result smaller.
- Simplify the final answer using the HCF, if possible.
In this guide
What is fraction multiplication?
Multiplying two fractions tells you what portion you get when you take a fraction of another fraction. Unlike adding or subtracting, you don't need a common denominator.
Why does multiplying fractions matter?
Multiplying fractions comes up whenever a portion applies to another portion, such as a discount on a discounted item, or the roses that make up part of the flower bed in a garden.
Multiplying two fractions that are each less than 1 always gives a smaller result, because you're taking a fraction of an already-partial amount.
The formula
| Symbol | What it means | Example |
|---|---|---|
| a | First fraction's numerator (top) | 3 |
| b | First fraction's denominator (bottom) | 5 |
| c | Second fraction's numerator | 2 |
| d | Second fraction's denominator | 3 |
How to multiply fractions step by step
- 1Multiply the two numerators (top numbers) together:
3 × 2 = 6. - 2Multiply the two denominators (bottom numbers) together:
5 × 3 = 15. - 3Write the results as a new fraction:
6/15. - 4Simplify the fraction by dividing both parts by their HCF:
6/15 = 2/5.
Enter your own two fractions in the calculator below to see every step.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Multiplying numerator by denominator instead of numerator by numerator. Keep tops with tops and bottoms with bottoms.
- Forgetting the result usually gets smaller. Since both fractions are less than 1, their product is a smaller portion of the whole.
- Leaving the answer unsimplified. Always check for a common factor between the final numerator and denominator.
Tips and tricks
- Multiplying by a whole number? Write it as a fraction over 1 first, like 4 becomes 4/1.
- Estimate first. Two fractions close to 1/2 should multiply to something close to 1/4.
- See also dividing fractions for the reverse operation, and adding fractions when you need a common denominator instead.
Where you'll use it in real life
- Gardening and design: finding a fraction of a fraction, like the roses within a flower bed.
- Cooking: scaling a recipe down to a fraction of its original size.
- Shopping: calculating a discount expressed as a fraction, like an extra 1/3 off an already reduced price.
- Construction: working out a fractional portion of a fractional measurement.
Quick summary
To multiply two fractions, multiply the numerators together, multiply the denominators together, and simplify the result. No common denominator is needed, and the answer is usually smaller than either starting fraction. Try the calculator above with your own two fractions.
Worked example
3/5 of your garden is planted with flowers. Of that flower area, 2/3 is roses. What fraction of the whole garden is roses?
- 01a/b × c/d = ac / bd
- 023/5 × 2/3 = (3×2) / (5×3)
- 03= 6/15
- 04Simplified = 2/5
- 05As a decimal = 0.4
These numbers are pre-filled in the calculator above.
Frequently asked questions
Do I need a common denominator to multiply fractions?
No. Multiplying fractions is simpler than adding them — just multiply the numerators together and the denominators together, no common denominator needed.
Why does multiplying two fractions give a smaller number?
Because each fraction represents less than one whole, taking a fraction of a fraction gives you an even smaller portion of the original whole.
How do I multiply a fraction by a whole number?
Write the whole number as a fraction over 1 (for example, 4 becomes 4/1), then multiply as usual — numerator by numerator and denominator by denominator.
Can multiplying two fractions ever give an answer bigger than 1?
Only if at least one of the fractions is greater than 1 (an improper fraction). Multiplying two fractions that are each less than 1 always gives a result less than 1.
