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).
• Internal link > Reduce common ordinary fractions to the lowest terms, online, with explanations
• Factor the numerators and the denominators of the reduced fractions: break them down to their prime factors.
• External link > Check whether numbers are prime or not. Calculate the prime factors of the composite 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.
• Internal link > Reduce (simplify) and write improper fractions as mixed numbers, online calculator
• Internal link > Multiply common ordinary fractions, online, with explanations

Internal link > Read the rest of the article, here: How to multiply common ordinary fractions?

(1) What is a fraction? Fractions types. How do they compare?

(2) Changing the form of fractions, by expanding or reducing (simplifying)

(3) How to reduce fractions (simplifying). The greatest common factor, GCF

(4) How to compare two fractions with unlike (different) numerators and denominators

(5) How to sort out fractions in ascending order

(6) Adding common (ordinary) fractions

(7) Subtracting common (ordinary) fractions

(8) Multiplying common (ordinary) fractions

(9) Fractions as rational numbers