Fraction Multiplication Calculator

Multiply fractions with step-by-step guidance: cross-cancel, multiply across, and auto-simplify to lowest terms or mixed numbers. Supports negatives and improper fractions.

Multiply Two Fractions

Your Results

Simplified Fraction

1/2

Steps

Cross-cancel: (2/3) × (3/4) → (1/1) × (1/2)
Product: 1/2 → Simplify to 1/2

How to Multiply Fractions

Standard Formula

Rule: (a/b) × (c/d) = (a×c) / (b×d)

Tip: Cross-cancel common factors before multiplying

Calculation Steps:

1
Cross-cancel
Reduce any common factors across diagonals
2
Multiply
Multiply numerators and denominators
3
Simplify
Reduce to lowest terms; convert to mixed number if improper

References

OpenStax. Prealgebra. Fractions & Mixed Numbers (LibreTexts/OpenStax). openstax.org
Common Core State Standards (CCSS) 5.NF.B.4 – Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction. corestandards.org
NCTM. Principles and Standards for School Mathematics – Number and Operations (Fractions). nctm.org

Important Considerations

Accuracy Tips

Always simplify; watch signs; avoid zero denominators.

✅ Best Practices

• Cross-cancel early
• Keep factors small
• Convert mixed to improper first

⚠️ Common Mistakes

• Adding denominators
• Forgetting to simplify
• Ignoring negative signs

Example Cases

Case 1: (2/3) × (3/4)

Cross-cancel → 2/1 × 1/4 → 2/4 → 1/2

Case 2: (-5/6) × (9/10)

Cross-cancel → (-1/2) × (3/2) = -3/4

Tips & Tricks

Keep Factors Small

Factor numbers and cancel early to avoid large intermediate products.

Handle Negatives

Odd number of negatives → negative result; even → positive.

Use Cases

Area/ratio scaling in geometry and recipes
Probability calculations with fractional chances
Algebraic manipulation with rational expressions

Frequently Asked Questions

How do you multiply fractions?

Multiply numerators together and denominators together, then simplify the result to lowest terms. Cross-cancel before multiplying to avoid large numbers.

What is cross-canceling?

Before multiplying, reduce by canceling any common factors between a numerator and the opposite denominator. This keeps numbers small and avoids overflow.

How do I handle negative fractions?

Count the number of negative signs. If it is odd, the result is negative; if even, the result is positive. Then multiply and simplify as usual.

Can the result be a mixed number?

Yes. If the simplified fraction is improper, convert it to a mixed number by dividing numerator by denominator and taking the remainder as the new numerator.

Do I need a common denominator to multiply?

No. Common denominators are only required for addition and subtraction. For multiplication, simply multiply straight across and simplify.