Multiplying ordinary (simple, common) math fractions, online calculator: multiplication of multiple fractions, the result explained

Multiply ordinary fractions, online calculator

The latest fractions multiplied

- 2 × - 5/6 × - 27/8 × 7/10 = ? Sep 16 14:04 UTC (GMT)
13/5 × 5 = ? Sep 16 14:04 UTC (GMT)
224 × - 3 × 8 × 5 = ? Sep 16 14:04 UTC (GMT)
2/5 × 15/32 × 8/9 = ? Sep 16 14:04 UTC (GMT)
13/5 × 5 = ? Sep 16 14:03 UTC (GMT)
2/5 × 15/32 × 8/9 = ? Sep 16 14:03 UTC (GMT)
3/8 × 5/32 = ? Sep 16 14:03 UTC (GMT)
5/12 × 240/25 = ? Sep 16 14:03 UTC (GMT)
15/20 × 7/10 × 4/21 = ? Sep 16 14:02 UTC (GMT)
8 × - 3/14 × 8 × - 5/21 × 8 × - 8/35 = ? Sep 16 14:02 UTC (GMT)
18/75 × 1/9 = ? Sep 16 14:00 UTC (GMT)
23/4 × 13/41 = ? Sep 16 13:58 UTC (GMT)
3/4 × 1,800 = ? Sep 16 13:58 UTC (GMT)
see more... ordinary fractions multiplied by users

Tutoring: multiplying fractions - how to multiply ordinary math fractions?

The end fraction will have:
  • - as a numerator, the result of multiplying all the fractions' numerators and
  • - as a denominator, the result of multiplying all the fractions' denominators.

Simply put, a/b × c/d = (a × c) / (b × d) - true if the numbers are coprime (no common prime factors); otherwise, the fractions should be reduced.

How to multiply ordinary fractions? Steps.

  • 1) Start by reducing fractions to lower terms (simplifying). Reduce ordinary math fractions to lower terms, online, with explanations.
  • 2) Factor the reduced fractions' numerators and denominators down to their prime factors. Calculate the prime factors of numbers, online calculator
  • 3) The end fraction will have: 1) as a numerator the product of all the numerators' prime factors and 2) as a denominator the product of all the denominators' prime factors.
  • 4) Reduce all the common prime factors of the factored numerators and denominators.
  • 5) Perform effectively the multiplication operations of the remaining prime factors above the fraction line, for the numerator, and under the line, for the denominator.
  • 6) The end fraction cannot be reduced anymore, since all the common prime factors were already reduced.
  • 7) Whenever the case, if the fraction is an improper one (also called a top-heavy fraction - numerator larger than denominator), the end fraction could be written as a mixed number (also called a mixed fraction), consisting of an integer and a proper fraction of the same sign.

An example of multiplying three ordinary fractions, with explanations: 6/90 × 80/24 × 30/75.

  • Reduce the first fraction to lowest terms (simplify): 6/90 = (2 × 3) / (2 × 32 × 5) = ((2 × 3) ÷ (2 × 3)) / ((2 × 32 × 5) ÷ (2 × 3)) = 1 / (3 × 5) = 1/15
  • Reduce the second fraction to lowest terms (simplify): 80/24 = (24 × 5) / (23 × 3) = ((24 × 5) ÷ (23)) / ((23 × 3) ÷ (23)) = (2 × 5) / 3 = 10/3
  • Reduce the third fraction to lowest terms (simplify): 30/75 = (2 × 3 × 5) / (3 × 52) = ((2 × 3 × 5) ÷ (3 × 5)) / ((3 × 52) ÷ (3 × 5)) = 2/5
  • At this point, fractions are reduced (simplified): 6/90 × 80/24 × 30/75 = 1 / (3 × 5) × (2 × 5) / 3 × 2/5
  • Effectively multiply all the fractions's numerators and denominators:

    1 / (3 × 5) × (2 × 5) / 3 × 2/5 = (1 × 2 × 2 × 5) / (3 × 3 × 5 × 5) = (2 × 2) / (3 × 3 × 5) = 4/45

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