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

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

#### Fraction: ^{76}/_{39} already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:

76 = 2^{2} × 19;

39 = 3 × 13;

#### Fraction: ^{71}/_{39} already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:

71 is a prime number, it cannot be factored into other prime factors;

39 = 3 × 13;

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

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

^{76}/_{39} × ^{71}/_{39} =

^{(76 × 71)} / _{(39 × 39)} =

^{(22 × 19 × 71)} / _{(3 × 13 × 3 × 13)} =

^{(22 × 19 × 71)} / _{(32 × 132)}

## Reduce (simplify) the 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 denominator have no common factors.

#### gcf(2^{2} × 19 × 71; 3^{2} × 13^{2}) = 1

### Divide the numerator and denominator by GCF.

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

^{(22 × 19 × 71)} / _{(32 × 132)} =

^{5,396}/_{1,521}

## Rewrite the fraction

### As a mixed number (also called a mixed fraction):

#### Mixed number = a whole number and a proper fraction, of the same sign.

#### Proper fraction = numerator smaller than denominator.

#### 5,396 ÷ 1,521 = 3 and remainder = 833 =>

#### 5,396 = 3 × 1,521 + 833 =>

^{5,396}/_{1,521} =

^{(3 × 1,521 + 833)}/_{1,521} =

^{(3 × 1,521)}/_{1,521} + ^{833}/_{1,521} =

#### 3 + ^{833}/_{1,521} =

#### 3 ^{833}/_{1,521}

### As a decimal number:

#### 3 + ^{833}/_{1,521} =

#### 3 + 833 ÷ 1,521 ≈

#### 3.547666009204 ≈

#### 3.55

### As a percentage:

#### 3.547666009204 =

#### 3.547666009204 × ^{100}/_{100} =

^{(3.547666009204 × 100)}/_{100} =

^{354.766600920447}/_{100} =

#### 354.766600920447% ≈

#### 354.77%

## The final answer:

:: written in four ways ::