## The executed operation (with ordinary fractions):

^{9}/_{21} × ^{16}/_{110}

### Reduce (simplify) fractions to their lowest terms equivalents:

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

#### Fraction: ^{9}/_{21} =

^{32}/_{(3 × 7)} =

^{(32 ÷ 3)}/_{((3 × 7) ÷ 3)} =

^{(32 ÷ 3)}/_{(3 ÷ 3 × 7)} =

^{3(2 - 1)}/_{(1 × 7)} =

^{31}/_{(1 × 7)} =

^{3}/_{(1 × 7)} =

^{3}/_{7};

#### Fraction: ^{16}/_{110} =

^{24}/_{(2 × 5 × 11)} =

^{(24 ÷ 2)}/_{((2 × 5 × 11) ÷ 2)} =

^{(24 ÷ 2)}/_{(2 ÷ 2 × 5 × 11)} =

^{2(4 - 1)}/_{(1 × 5 × 11)} =

^{23}/_{(1 × 5 × 11)} =

^{8}/_{55};

### Rewrite the equivalent simplified operation:

^{9}/_{21} × ^{16}/_{110} =

^{3}/_{7} × ^{8}/_{55}

### Multiply the numerators and the denominators of the fractions separately:

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

^{3}/_{7} × ^{8}/_{55} =

^{(3 × 8)} / _{(7 × 55)} =

^{(3 × 23)} / _{(7 × 5 × 11)} =

^{(23 × 3)} / _{(5 × 7 × 11)}

## Reduce (simplify) fraction to its lowest terms equivalent:

### Calculate the greatest common factor, GCF:

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

#### But, the numerator and the denominator have no common factors

#### gcf(2^{3} × 3; 5 × 7 × 11) = 1

### Divide the numerator and the denominator by GCF.

#### The numerator and the denominator of the fraction are coprime numbers (no common prime factors, GCF = 1), the fraction cannot be reduced (simplified): irreducible fraction.

^{(23 × 3)} / _{(5 × 7 × 11)} =

^{24}/_{385}

## Rewrite the fraction