## The executed operation (with ordinary fractions):

^{33}/_{2} × ^{16}/_{11}

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

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

#### Fraction: ^{33}/_{2} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

33 = 3 × 11;

2 is a prime number;

#### Fraction: ^{16}/_{11} already reduced to the lowest terms.

The numerator and the denominator have no common prime factors.

Their prime factorization:

16 = 2^{4};

11 is a prime number;

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

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

^{33}/_{2} × ^{16}/_{11} =

^{(33 × 16)} / _{(2 × 11)} =

^{(3 × 11 × 24)} / _{(2 × 11)} =

^{(24 × 3 × 11)} / _{(2 × 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.

#### gcf(2^{4} × 3 × 11; 2 × 11) = 2 × 11

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

^{(24 × 3 × 11)} / _{(2 × 11)} =

^{((24 × 3 × 11) ÷ (2 × 11))} / _{((2 × 11) ÷ (2 × 11))} =

^{(24 ÷ 2 × 3 × 11 ÷ 11)}/_{(2 ÷ 2 × 11 ÷ 11)} =

^{(2(4 - 1) × 3 × 1)}/_{(1 × 1)} =

^{(23 × 3 × 1)}/_{(1 × 1)} =

^{(23 × 3)}/_{1} =

#### 8 × 3 =

#### 24;

## Rewrite the end result: