## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{260}/_{186}

#### The number above the bar is the numerator: 260

#### The number below the bar is the denominator: 186

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

^{260}/_{186} = 260 ÷ 186

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

Value = 260 ÷ 186

### 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.

#### 260 = 2^{2} × 5 × 13;

260 is not a prime, is a composite number;

#### 186 = 2 × 3 × 31;

186 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 (260; 186) = 2

## 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.

#### 130 ÷ 93 = 1 and remainder = 37 =>

#### 130 = 1 × 93 + 37 =>

^{130}/_{93} =

^{(1 × 93 + 37)} / _{93} =

^{(1 × 93)} / _{93} + ^{37} / _{93} =

#### 1 + ^{37}/_{93} =

#### 1 ^{37}/_{93}

### As a decimal number:

#### 1 ^{37}/_{93} =

#### 1 + ^{37}/_{93} =

#### 1 + 37 ÷ 93 ≈

#### 1.397849462366 ≈

#### 1.4

### As a percentage:

#### 1.397849462366 =

#### 1.397849462366 × ^{100}/_{100} =

#### ^{139.784946236559}/_{100} =

#### 139.784946236559% ≈

#### 139.78%

#### 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...