## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{88,920}/_{62,613}

#### The number above the bar is the numerator: 88,920

#### The number below the bar is the denominator: 62,613

#### The fraction bar means that the two numbers are dividing themselves:

^{88,920}/_{62,613} = 88,920 ÷ 62,613

#### Divide the numerator by the denominator to get fraction's value:

Value = 88,920 ÷ 62,613

### Introduction. Percent

#### 'Percent (%)' means 'out of one hundred':

#### p% = p 'out of one hundred',

#### p% = ^{p}/_{100} = p ÷ 100

### Note:

#### The fraction ^{100}/_{100} = 100 ÷ 100 = 100% = 1

#### Multiply a number by the fraction ^{100}/_{100},

... and its value doesn't change.

## To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

#### To calculate the greatest common factor, we build the prime factorization of the two numbers.

### Integer numbers prime factorization:

#### Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

#### 88,920 = 2^{3} × 3^{2} × 5 × 13 × 19;

88,920 is not a prime, is a composite number;

#### 62,613 = 3^{4} × 773;

62,613 is not a prime, is a composite number;

** Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself. *

* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.

### Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

#### Multiply all the common prime factors, by the lowest exponents (if any).

#### gcf, hcf, gcd (88,920; 62,613) = 3^{2} = 9

### Divide both the numerator and the denominator by their greatest common factor.

^{88,920}/_{62,613} =

^{(23 × 32 × 5 × 13 × 19)}/_{(34 × 773)} =

^{((23 × 32 × 5 × 13 × 19) ÷ 32)} / _{((34 × 773) ÷ 32)} =

^{(23 × 5 × 13 × 19)}/_{(32 × 773)} =

^{9,880}/_{6,957}

## The fraction is now reduced to the lowest terms.

^{9,880}/_{6,957} is an improper fraction.

#### An improper fraction: numerator larger than denominator.

## Rewrite the end result, continued below...

## Rewrite the fraction:

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

#### A mixed number (mixed fraction): a whole number and a proper fraction, of the same sign.

#### A proper fraction: numerator smaller than denominator.

#### 9,880 ÷ 6,957 = 1 and remainder = 2,923 =>

#### 9,880 = 1 × 6,957 + 2,923 =>

^{9,880}/_{6,957} =

^{(1 × 6,957 + 2923)} / _{6,957} =

^{(1 × 6,957)} / _{6,957} + ^{2923} / _{6,957} =

#### 1 + ^{2,923}/_{6,957} =

#### 1 ^{2,923}/_{6,957}

### As a decimal number:

#### 1 ^{2,923}/_{6,957} =

#### 1 + ^{2,923}/_{6,957} =

#### 1 + 2,923 ÷ 6,957 ≈

#### 1.420152364525 ≈

#### 1.42

### As a percentage:

#### 1.420152364525 =

#### 1.420152364525 × ^{100}/_{100} =

#### ^{142.015236452494}/_{100} =

#### 142.015236452494% ≈

#### 142.02%

#### In other words:

#### 1) Calculate fraction's value.

#### 2) Multiply that number by 100.

#### 3) Add the percent sign % to it.

## Final answer

continued below...