Multiplying Fractions Calculator
Multiply two fractions step by step: multiply numerators, multiply denominators, then simplify by dividing both by their GCD. Includes the decimal equivalent and a fraction-bar view.
Multiply numerators together
Multiply denominators together
Form the raw product
Divide both by GCD = 6
Simplified fraction
- 1
Multiply numerators
2 × 3 = 6 - 2
Multiply denominators
3 × 4 = 12 - 3
GCD of 6 and 12
6Dividing both parts by their GCD reduces the fraction to lowest terms. - 4
Simplified fraction as decimal
1 ÷ 2 = 0.500000
How does this calculator work?
Multiply fractions by multiplying numerators together and denominators together: (a/b) × (c/d) = (a·c)/(b·d). Then simplify by dividing both parts by their GCD. No common denominator is needed — multiplication goes straight across. Decimal equivalent and fraction-bar view are shown for the simplified result.
Formula
How this is calculated
Multiplying fractions is the simplest of the four fraction operations: multiply the two numerators together to get the product numerator, then multiply the two denominators together to get the product denominator. There is no need for a common denominator. The formula is (a/b) × (c/d) = (a·c)/(b·d).
The raw product is then reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). For example, (2/3) × (3/4) = 6/12, and GCD(6, 12) = 6, so the simplified result is 1/2. Alternatively you can cross-cancel before multiplying — divide a numerator and the opposite denominator by their GCD first — which keeps the intermediate numbers smaller, but both approaches give the same simplified answer.
The result is exact integer arithmetic when all four inputs are integers. Denominators of zero are undefined and rejected. If the simplified denominator is 1, the fraction is a whole number and is displayed as such. The fraction bar visualises the result as a proportion of the whole denominator for proper fractions.
Frequently asked questions
Addition requires a common denominator (you must align the denominators first), which adds steps. Multiplication just goes straight across: numerator times numerator, denominator times denominator. You only need to simplify afterwards, not before.
Cross-cancelling means dividing a numerator in one fraction and a denominator in the other by their GCD before multiplying. For example, 2/3 × 3/4 — you can cancel the 3 in the numerator of the second fraction with the 3 in the denominator of the first, giving 2/1 × 1/4 = 2/4 = 1/2. It reduces the numbers you multiply but gives the same final result as simplifying afterwards.
Write the whole number as a fraction with denominator 1, then multiply normally. For example, 5 × (2/3) = (5/1) × (2/3) = 10/3. In this calculator, enter 5 for the numerator and 1 for the denominator of one of the fractions.
Also known as
TG we-Calculate Editorial Team. (2026). Multiplying Fractions Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/multiplying-fractions-calculator
TG we-Calculate Editorial Team. "Multiplying Fractions Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/multiplying-fractions-calculator.
TG we-Calculate Editorial Team, "Multiplying Fractions Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/multiplying-fractions-calculator
@misc{wecalculate_multiplying_fractions_calculator, title = {Multiplying Fractions Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/multiplying-fractions-calculator}}, year = {2026}, note = {TG we-Calculate} }
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