## 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 = 2^{5};

#### Fraction: ^{16}/_{27} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

16 = 2^{4};

27 = 3^{3};

### 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)}

## 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(2^{4} × 3 × 5; 2^{5} × 3^{3}) = 2^{4} × 3

### 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};

## Rewrite the fraction