## The operation of comparing fractions:

^{69}/_{94} vs. ^{78}/_{104}

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

^{69}/_{94} already reduced to the lowest terms;

the numerator and the denominator have no common prime factors:

69 = 3 × 23;

94 = 2 × 47;

^{78}/_{104} = ^{(2 × 3 × 13)}/_{(23 × 13)} = ^{((2 × 3 × 13) ÷ (2 × 13))}/_{((23 × 13) ÷ (2 × 13))} = ^{3}/_{4};

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

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

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

#### The prime factorization of the numerators:

#### 69 = 3 × 23;

#### 3 is a prime number;

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

#### LCM (69, 3) = 3 × 23 = 69

### Calculate the expanding number of each fraction

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

#### For fraction: ^{69}/_{94} is 69 ÷ 69 = (3 × 23) ÷ (3 × 23) = 1;

#### For fraction: ^{3}/_{4} is 69 ÷ 3 = (3 × 23) ÷ 3 = 23;

### Expand the fractions

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

#### Multiply the numerators and the denominators by their expanding number:

^{69}/_{94} = ^{(1 × 69)}/_{(1 × 94)} = ^{69}/_{94};

^{3}/_{4} = ^{(23 × 3)}/_{(23 × 4)} = ^{69}/_{92};

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

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

## ::: Comparing operation :::

The final answer: