## The operation of comparing fractions:

^{11}/_{38} and ^{20}/_{47}

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

^{11}/_{38} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

11 is a prime number;

38 = 2 × 19;

^{20}/_{47} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

20 = 2^{2} × 5;

47 is a prime number;

## To sort fractions, build them up to the same numerator.

### Calculate LCM, the least common multiple of the fractions' numerators

#### LCM will be the common numerator of the compared fractions.

#### The prime factorization of the numerators:

#### 11 is a prime number

#### 20 = 2^{2} × 5

#### Multiply all the unique prime factors, by the largest exponents:

#### LCM (11, 20) = 2^{2} × 5 × 11 = 220

### Calculate the expanding number of each fraction

#### Divide LCM by the numerator of each fraction:

#### For fraction: ^{11}/_{38} is 220 ÷ 11 = (2^{2} × 5 × 11) ÷ 11 = 20

#### For fraction: ^{20}/_{47} is 220 ÷ 20 = (2^{2} × 5 × 11) ÷ (2^{2} × 5) = 11

### Expand the fractions

#### Build up all the fractions to the same numerator (which is LCM).

Multiply the numerators and denominators by their expanding number:

^{11}/_{38} = ^{(20 × 11)}/_{(20 × 38)} = ^{220}/_{760}

^{20}/_{47} = ^{(11 × 20)}/_{(11 × 47)} = ^{220}/_{517}

### The fractions have the same numerator, compare their denominators.

#### The larger the denominator the smaller the positive fraction.

## ::: Comparing operation :::

The final answer: