## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{290}/_{205}

#### The number above the bar is the numerator: 290

#### The number below the bar is the denominator: 205

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

^{290}/_{205} = 290 ÷ 205

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

Value = 290 ÷ 205

### 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.

#### 290 = 2 × 5 × 29;

290 is not a prime, is a composite number;

#### 205 = 5 × 41;

205 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 (290; 205) = 5

## 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.

#### 58 ÷ 41 = 1 and remainder = 17 =>

#### 58 = 1 × 41 + 17 =>

^{58}/_{41} =

^{(1 × 41 + 17)} / _{41} =

^{(1 × 41)} / _{41} + ^{17} / _{41} =

#### 1 + ^{17}/_{41} =

#### 1 ^{17}/_{41}

### As a decimal number:

#### 1 ^{17}/_{41} =

#### 1 + ^{17}/_{41} =

#### 1 + 17 ÷ 41 ≈

#### 1.414634146341 ≈

#### 1.41

### As a percentage:

#### 1.414634146341 =

#### 1.414634146341 × ^{100}/_{100} =

#### ^{141.463414634146}/_{100} =

#### 141.463414634146% ≈

#### 141.46%

#### 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...