Multiply two fractions together.
Numerators multiply together, and denominators multiply together — no common denominator needed.
Product: a/b × c/d = (a×c) ÷ (b×d)
A fraction multiplication calculator multiplies two fractions and returns the product in lowest terms, along with its decimal value. It multiplies the numerators together and the denominators together, then reduces. No common denominator is needed.
Multiplying fractions answers 'a fraction of a fraction' questions. What is 4/5 of 15/16 of a kilogram? What share does each of three partners own if one holds 2/3 of a half-share? It is also how you scale a recipe by a fractional factor, find the probability of two independent events, and compute area when both sides are fractional lengths. In the NCERT Class 7 syllabus, 'of' is explicitly taught as meaning multiplication.
1. Write the fractions as a/b and c/d.
2. Cancel first if you can: divide any numerator and any denominator by a common factor.
3. Multiply the numerators: a × c.
4. Multiply the denominators: b × d.
5. Write the product (a × c) ÷ (b × d) and reduce it by the HCF of the new numerator and denominator.
6. Convert to a mixed number if the product is improper and the question asks for it.
Taking 4/5 of something means splitting it into 5 equal parts and keeping 4. If the something is 15/16, splitting it into 5 parts divides each sixteenth into five, making eightieths, and keeping 4 of every 5 parts leaves 4 × 15 eightieths. So 4/5 of 15/16 = 60/80. Drawing this as a rectangle, with one fraction shading columns and the other shading rows, shows the overlap directly and is a common Class 7 visual.
Because multiplication is commutative, (a × c) ÷ (b × d) can be rearranged as (a ÷ d) × (c ÷ b) whenever those divisions are exact. That is why you may cancel a numerator against the other fraction's denominator. In 4/5 × 15/16, 4 cancels with 16 to leave 1/4, and 15 cancels with 5 to leave 3/1, giving 3/4 without ever writing 60/80. The calculator multiplies first and reduces at the end, which reaches the same result.
When both fractions are between 0 and 1, the product is smaller than either of them, because you are taking a part of a part. This surprises students who expect multiplication to make things bigger. If one factor is greater than 1, the product is larger than the other factor. The same idea underlies probability: the chance that two independent events both happen is the product of their probabilities, and so it is smaller than either one alone.
Harish has 15/16 of a kilogram of cashews and packs 4/5 of it into gift boxes for Diwali.
Starting point: 4/5 × 15/16
Multiply across the top and bottom: (4 × 15) / (5 × 16) = 60/80
Reduce to lowest terms: Divide both by their GCD of 20 → 3/4
Answer: Result 3/4
Finding a common denominator first, which is unnecessary and adds work.
Cancelling a numerator against its own denominator incorrectly, or cancelling across a plus sign.
Multiplying a whole number into both the top and the bottom, such as 3 × 2/5 = 6/15.
Expecting the product of two proper fractions to be bigger than both.
Finding a fraction of a quantity, such as 4/5 of a stock of goods.
Scaling recipes by fractional factors.
Computing probabilities of two independent events.
Areas of rectangles with fractional side lengths.
Share calculations in partnerships and inheritance.
Why doesn't multiplying fractions need a common denominator?
Unlike addition, multiplying does not need the pieces to be the same size — you are simply combining two scaling numbers directly.