## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{74,692}/_{29,878}

#### The number above the bar is the numerator: 74,692

#### The number below the bar is the denominator: 29,878

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

^{74,692}/_{29,878} = 74,692 ÷ 29,878

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

Value = 74,692 ÷ 29,878

### 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.

#### 74,692 = 2^{2} × 71 × 263;

74,692 is not a prime, is a composite number;

#### 29,878 = 2 × 14,939;

29,878 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 (74,692; 29,878) = 2

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

^{74,692}/_{29,878} =

^{(22 × 71 × 263)}/_{(2 × 14,939)} =

^{((22 × 71 × 263) ÷ 2)} / _{((2 × 14,939) ÷ 2)} =

^{(2 × 71 × 263)}/_{14,939} =

^{37,346}/_{14,939}

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

^{37,346}/_{14,939} 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.

#### 37,346 ÷ 14,939 = 2 and remainder = 7,468 =>

#### 37,346 = 2 × 14,939 + 7,468 =>

^{37,346}/_{14,939} =

^{(2 × 14,939 + 7468)} / _{14,939} =

^{(2 × 14,939)} / _{14,939} + ^{7468} / _{14,939} =

#### 2 + ^{7,468}/_{14,939} =

#### 2 ^{7,468}/_{14,939}

### As a decimal number:

#### 2 ^{7,468}/_{14,939} =

#### 2 + ^{7,468}/_{14,939} =

#### 2 + 7,468 ÷ 14,939 ≈

#### 2.499899591673 ≈

#### 2.5

### As a percentage:

#### 2.499899591673 =

#### 2.499899591673 × ^{100}/_{100} =

#### ^{249.98995916728}/_{100} =

#### 249.98995916728% ≈

#### 249.99%

#### 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...