## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{105}/_{100}

#### The number above the bar is the numerator: 105

#### The number below the bar is the denominator: 100

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

^{105}/_{100} = 105 ÷ 100

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

Value = 105 ÷ 100

### 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.

## 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.

#### 21 ÷ 20 = 1 and remainder = 1 =>

#### 21 = 1 × 20 + 1 =>

^{21}/_{20} =

^{(1 × 20 + 1)} / _{20} =

^{(1 × 20)} / _{20} + ^{1} / _{20} =

#### 1 + ^{1}/_{20} =

#### 1 ^{1}/_{20}

### As a decimal number:

#### 1 ^{1}/_{20} =

#### 1 + ^{1}/_{20} =

#### 1 + 1 ÷ 20 =

#### 1.05

### As a percentage:

#### 1.05 =

#### 1.05 × ^{100}/_{100} =

#### ^{105}/_{100} =

#### 105%

#### 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...