Multiply fractions, online calculator: multiplication of ordinary (simple, common) fractions, explained result

Multiply ordinary fractions, online calculator

Multiplying fractions. How to multiply ordinary math fractions? Steps. Example.

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

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