## The operation of comparing fractions:

^{70}/_{97} and ^{78}/_{102}

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

^{70}/_{97} already reduced to the lowest terms;

the numerator and denominator have no common prime factors:

70 = 2 × 5 × 7;

97 is a prime number;

^{78}/_{102} = ^{(2 × 3 × 13)}/_{(2 × 3 × 17)} = ^{((2 × 3 × 13) ÷ (2 × 3))}/_{((2 × 3 × 17) ÷ (2 × 3))} = ^{13}/_{17}

## 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:

#### 70 = 2 × 5 × 7

#### 13 is a prime number

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

#### LCM (70, 13) = 2 × 5 × 7 × 13 = 910

### Calculate the expanding number of each fraction

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

#### For fraction: ^{70}/_{97} is 910 ÷ 70 = (2 × 5 × 7 × 13) ÷ (2 × 5 × 7) = 13

#### For fraction: ^{13}/_{17} is 910 ÷ 13 = (2 × 5 × 7 × 13) ÷ 13 = 70

### Expand the fractions

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

Multiply the numerators and denominators by their expanding number:

^{70}/_{97} = ^{(13 × 70)}/_{(13 × 97)} = ^{910}/_{1,261}

^{13}/_{17} = ^{(70 × 13)}/_{(70 × 17)} = ^{910}/_{1,190}

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

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

## ::: Comparing operation :::

The final answer: