How to Multiply Fractions
Learn how to multiply fractions by multiplying numerators and denominators, simplifying, using examples, avoiding mistakes, and checking answers.
Quick Answer
To multiply fractions, multiply the numerators together, multiply the denominators together, then simplify the result. For mixed numbers, convert them to improper fractions first.
What You Need
- Pencil
- Paper
- Fractions to multiply
- Basic multiplication facts
- Simplifying method
Safety Precautions
- Check whether numbers are mixed numbers before multiplying.
- Do not cross-multiply; that is for comparing or solving proportions.
- Simplify only by dividing numerator and denominator by the same factor.
- Keep negative signs consistent.
- Show work for school assignments.
Step-by-Step Instructions
- Step 1
Write the fractions
Place the fractions side by side with a multiplication sign.
- Step 2
Convert mixed numbers
Change mixed numbers into improper fractions first.
- Step 3
Multiply numerators
Multiply the top numbers together.
- Step 4
Multiply denominators
Multiply the bottom numbers together.
- Step 5
Simplify
Divide numerator and denominator by common factors.
- Step 6
Convert if needed
Change an improper fraction to a mixed number if requested.
- Step 7
Check reasonableness
Estimate whether the answer size makes sense.
Practical Example
Example: 2/3 x 3/4 = 6/12, which simplifies to 1/2.
Common Mistakes
- Adding instead of multiplying denominators
- Cross-multiplying
- Forgetting mixed numbers
- Not simplifying
- Dropping negative signs
- Simplifying incorrectly
Troubleshooting
Answer is not simplified
Find a common factor and divide top and bottom by it.
Mixed number is confusing
Convert it to an improper fraction before multiplying.
Numbers get large
Cancel common factors diagonally before multiplying if allowed.
Negative signs confuse you
One negative makes a negative answer; two negatives make positive.
Helpful Internal Links
FAQs
Do denominators need to be the same?
No. Unlike addition, fraction multiplication does not require common denominators.
Can I simplify before multiplying?
Yes, canceling common factors before multiplying can make the work easier.
How do I multiply mixed numbers?
Convert each mixed number to an improper fraction first.
What is 1/2 times 1/2?
It is 1/4.
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