# Multiply fractions, online calculator: the result of multiplication explained

## The latest fractions multiplied

 8/14 × - 19/21 = ? Oct 29 22:11 UTC (GMT) - 47/73 × - 92/71 = ? Oct 29 22:11 UTC (GMT) 7/8 × 6/7 = ? Oct 29 22:11 UTC (GMT) - 659/32 × - 27/25 = ? Oct 29 22:11 UTC (GMT) 23/48 × - 23/31 = ? Oct 29 22:11 UTC (GMT) 27/127 × 49/20 = ? Oct 29 22:11 UTC (GMT) 78/55 × - 53/89 × 35/102 = ? Oct 29 22:11 UTC (GMT) 4/5 × 640 = ? Oct 29 22:11 UTC (GMT) - 118/7 × 9/32 = ? Oct 29 22:10 UTC (GMT) 71/24 × 58/22 = ? Oct 29 22:10 UTC (GMT) - 16/18 × 102/8 = ? Oct 29 22:10 UTC (GMT) - 35/25 × 16/28 = ? Oct 29 22:10 UTC (GMT) 33/14 × 66/28 = ? Oct 29 22:10 UTC (GMT) see more... ordinary (common) fractions multiplied by users

## How to multiply two fractions?

#### When we multiply ordinary fractions, the end fraction will have:

• as a numerator, the result of multiplying all the numerators of the fractions,
• as a denominator, the result of multiplying all the denominators of the fractions.
• a/b × c/d = (a × c) / (b × d)
• a, b, c, d are integer numbers;
• if the pairs (a × c) and (b × d) are not coprime (they have common prime factors) the end fraction should be reduced (simplified) to lower terms.

### How to multiply ordinary fractions? Steps.

• Start by reducing fractions to lower terms (simplifying).
• Reduce math fractions to lower terms, online, with explanations.
• Factor the numerators and the denominators of the reduced fractions: break them down to their prime factors.
• Calculate the prime factors of numbers, online calculator
• Above the fraction bar we write the product of all the prime factors of the fractions' numerators, without doing any calculations.
• Below the fraction bar we write the product of all the prime factors of the fractions' denominators, without doing any calculations.
• Cross out all the common prime factors that appear both above and below the fraction bar.
• Multiply the remaining prime factors above the fraction bar - this will be the numerator of the resulted fraction.
• Multiply the remaining prime factors below the fraction bar - this will be the denominator of the resulted fraction.
• There is no need to reduce (simplify) the resulting fraction, since we have already crossed out all the common prime factors.
• If the resulted fraction is an improper one (without considering the sign, the numerator is larger than the denominator), it could be written as a mixed number, consisting of an integer and a proper fraction of the same sign.
• Write improper fractions as mixed numbers, online.
• Multiply ordinary fractions, online, with explanations.

### An example of multiplying three ordinary fractions, with explanations:

• 6/90 × 80/24 × 30/75 = ?
• Factor the numerators and the denominators of the fractions (break them down as products of prime factors) and reduce the original fractions.
• 6/90 = (2 × 3) / (2 × 32 × 5) = ((2 × 3) ÷ (2 × 3)) / ((2 × 32 × 5) ÷ (2 × 3)) = 1/(3 × 5) = 1/15
• 80/24 = (24 × 5) / (23 × 3) = ((24 × 5) ÷ (23)) / ((23 × 3) ÷ (23)) = (2 × 5)/3 = 10/3
• 30/75 = (2 × 3 × 5) / (3 × 52) = ((2 × 3 × 5) ÷ (3 × 5)) / ((3 × 52) ÷ (3 × 5)) = 2/5
• At this point, the fractions are reduced (simplified) and their numerators and denominators are factored:
• 6/90 × 80/24 × 30/75 = 1/(3 × 5) × (2 × 5)/3 × 2/5
• Multiply all the prime factors above and respectively below the fraction bar, crossing out the common factors:
• 1/(3 × 5) × (2 × 5)/3 × 2/5
• = (1 × 2 × 5 × 2) / (3 × 5 × 3 × 5)
• = (1 × 2 × 2 × 5) / (3 × 3 × 5 × 5)
• = (1 × 2 × 2 × 5) / (3 × 3 × 5 × 5)
• = (2 × 2) / (3 × 3 × 5)
• = 4/45