Multiply fractions: ^{10}/_{15} × - ^{250,008}/_{5} = ? Multiplication result of the ordinary (simple, common) fractions explained

^{10}/_{15} × - ^{250,008}/_{5} = ?

Rewrite the equivalent simplified operation:

Combine the signs of the fractions into a single one, placed in front of the expression.

The sign of the multiplication: + 1 × + 1 = + 1; + 1 × - 1 = - 1; - 1 × - 1 = + 1.

^{10}/_{15} × - ^{250,008}/_{5} =

- ^{10}/_{15} × ^{250,008}/_{5}

Reduce (simplify) fractions to their lowest terms equivalents:

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

Fraction: ^{10}/_{15} =

^{(2 × 5)}/_{(3 × 5)} =

^{((2 × 5) ÷ 5)}/_{((3 × 5) ÷ 5)} =

^{(2 × 5 ÷ 5)}/_{(3 × 5 ÷ 5)} =

^{(2 × 1)}/_{(3 × 1)} =

^{2}/_{3};

Fraction: ^{250,008}/_{5} already reduced to the lowest terms. The numerator and denominator have no common prime factors. Their prime factorization: 250,008 = 2^{3} × 3 × 11 × 947; 5 is a prime number, it cannot be factored into other prime factors;

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.