## 1. Write the number as a percentage.

#### Note: ^{100}/_{100} = 1

#### 52.8 =

#### 52.8 × ^{100}/_{100} =

^{(52.8 × 100)}/_{100} =

#### ^{5,280}/_{100} =

#### 5,280%

#### In other words:

#### Multiply the number by 100...

#### ... And then add the percent sign, %

#### 52.8 = 5,280%

## 2. Write the number as an improper fraction.

#### 52.8 can be written as an improper fraction.

#### (The numerator is larger than or equal to the denominator).

### Write down the number divided by 1, as a fraction:

#### 52.8 = ^{52.8}/_{1}

### Turn the top number into a whole number.

#### Multiply both the top and the bottom by the same number.

#### This number is: 10.

#### (1 followed by as many 0s as the number of digits after the decimal point)

^{52.8}/_{1} =

^{(52.8 × 10)}/_{(1 × 10)} =

^{528}/_{10}

## 3. Reduce (simplify) the fraction above: ^{528}/_{10}

(to the lowest terms, to its simplest equivalent form, irreducible).

#### To reduce a fraction divide the numerator and the denominator by their greatest (highest) common factor (divisor), GCF.

### Factor both the numerator and the denominator (prime factorization).

#### In exponential notation (a^{n}):

#### 528 = 2^{4} × 3 × 11

#### 10 = 2 × 5

### Calculate the greatest (highest) common factor (divisor), GCF.

#### Multiply all the common prime factors by the lowest exponents.

#### GCF (2^{4} × 3 × 11; 2 × 5) = 2

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

^{528}/_{10} =

^{(24 × 3 × 11)}/_{(2 × 5)} =

^{((24 × 3 × 11) ÷ 2)} / _{((2 × 5) ÷ 2)} =

^{(23 × 3 × 11)}/_{5} =

^{264}/_{5}

## 4. The fraction is an improper one, rewrite it as a mixed number (mixed fraction):

#### A mixed number = an integer number and a proper fraction, of the same sign.

#### Example 1: 2 ^{1}/_{5}; Example 2: - 1 ^{3}/_{7}.

#### A proper fraction = the numerator is smaller than the denominator.

#### 264 ÷ 5 = 52, remainder = 4 =>

#### 264 = 52 × 5 + 4 =>

#### ^{264}/_{5} =

#### ^{(52 × 5 + 4)} / _{5} =

^{(52 × 5)} / _{5} + ^{4}/_{5} =

#### 52 + ^{4}/_{5} =

#### 52 ^{4}/_{5}

^{264}/_{5}: Equivalent fractions.

#### The above fraction cannot be reduced.

#### That is, it has the smallest numerator and denominator possible.

#### By expanding it we can build up equivalent fractions.

#### (Multiply the numerator & the denominator by the same number).

### Example 1. By expanding the fraction by 5:

^{264}/_{5} = ^{(264 × 5)}/_{(5 × 5)} = ^{1,320}/_{25}

### Example 2. By expanding the fraction by 8:

^{264}/_{5} = ^{(264 × 8)}/_{(5 × 8)} = ^{2,112}/_{40}

#### Of course, the above fractions are reducing...

#### ... to the initial fraction: ^{264}/_{5}