Multiply Fractions Calculator – Fraction Multiplication
Multiply fractions and simplify the result.
Table of Contents
How to Use
- Enter the numerator and denominator of the first fraction
- Enter the numerator and denominator of the second fraction
- Click calculate to multiply the fractions
- View the simplified result, decimal form, and steps
How to Multiply Fractions
Multiplying fractions is straightforward: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
Formula: (a/b) × (c/d) = (a × c) / (b × d)
For example: (2/3) × (4/5) = (2 × 4) / (3 × 5) = 8/15
Simplifying the Result
After multiplying, always simplify the result by dividing both the numerator and denominator by their greatest common divisor (GCD).
- Find the GCD of the numerator and denominator
- Divide both by the GCD
- The result is the simplified fraction
Converting to Mixed Numbers
If the result is an improper fraction (numerator larger than denominator), it can be converted to a mixed number:
- Divide the numerator by the denominator
- The quotient is the whole number part
- The remainder over the original denominator is the fractional part
Tips for Easier Multiplication
You can simplify before multiplying by canceling common factors diagonally:
- Look for common factors between numerator of one fraction and denominator of the other
- Cancel these common factors before multiplying
- This results in smaller numbers and easier calculation
Frequently Asked Questions
- Do I need a common denominator to multiply fractions?
- No! Unlike addition and subtraction, multiplication does not require a common denominator. Simply multiply numerators together and denominators together.
- What if one of my fractions is negative?
- The rules for signs apply: positive × positive = positive, negative × negative = positive, and positive × negative = negative. The calculator handles negative numbers automatically.
- How do I multiply a whole number by a fraction?
- Convert the whole number to a fraction by putting it over 1. For example, 3 × (2/5) = (3/1) × (2/5) = 6/5.
- Why should I simplify before multiplying?
- Simplifying before multiplying (cross-canceling) keeps the numbers smaller and makes the calculation easier. The final answer will be the same either way.