Multiply fractions: 15/32 × 16/27 = ? Multiplication result of the ordinary (simple, common) fractions explained

The executed operation (with ordinary fractions):
15/32 × 16/27

Reduce (simplify) fractions to their lowest terms equivalents:

Factor all the numbers in order to easily reduce (simplify) the end fraction.

Fraction: 15/32 already reduced to the lowest terms.
The numerator and the denominator have no common prime factors.
Their prime factorization:
15 = 3 × 5;
32 = 25;


Fraction: 16/27 already reduced to the lowest terms.
The numerator and the denominator have no common prime factors.
Their prime factorization:
16 = 24;
27 = 33;


>> Reduce (simplify) fractions to their simplest form, online calculator


Multiply the numerators and the denominators of the fractions separately:

Factor all the numbers in order to easily reduce (simplify) the end fraction.

15/32 × 16/27 =


(15 × 16) / (32 × 27) =


(3 × 5 × 24) / (25 × 33) =


(24 × 3 × 5) / (25 × 33)

>> Calculate the prime factors of numbers, online calculator


Reduce (simplify) fraction to its lowest terms equivalent:

Calculate the greatest common factor, GCF:

Multiply all the common prime factors, by the lowest exponents.


gcf(24 × 3 × 5; 25 × 33) = 24 × 3

>> Calculate the greatest common factor, GCF, online calculator


Divide the numerator and the denominator by GCF.

(24 × 3 × 5) / (25 × 33) =


((24 × 3 × 5) ÷ (24 × 3)) / ((25 × 33) ÷ (24 × 3)) =


(24 ÷ 24 × 3 ÷ 3 × 5)/(25 ÷ 24 × 33 ÷ 3) =


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


(20 × 1 × 5)/(2 × 32) =


(1 × 1 × 5)/(2 × 32) =


5/(2 × 32) =


5/(2 × 9) =


5/18;

>> Reduce (simplify) fractions to their simplest form, online calculator


Rewrite the fraction

As a decimal number:

5/18 =


5 ÷ 18 ≈


0.277777777778 ≈


0.28

As a percentage:

0.277777777778 =


0.277777777778 × 100/100 =


(0.277777777778 × 100)/100 =


27.777777777778/100


27.777777777778% ≈


27.78%

>> Convert fractions to percentages, online calculator


The final answer:
:: written in three ways ::

As a positive proper fraction (numerator < denominator):
15/32 × 16/27 = 5/18

As a decimal number:
15/32 × 16/27 ≈ 0.28

As a percentage:
15/32 × 16/27 ≈ 27.78%

How to multiply the ordinary fractions:
17/40 × 18/35

Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark; numbers rounded to max. 12 decimals (whenever the case);

Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; ≈ approximation;

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.

... Read the rest of this article, here: How to multiply ordinary (common) fractions?

More on ordinary (common) math fractions theory: