## 1. Write the number as a percentage.

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

#### 29.55 =

#### 29.55 × ^{100}/_{100} =

^{(29.55 × 100)}/_{100} =

#### ^{2,955}/_{100} =

#### 2,955%

#### In other words:

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

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

#### 29.55 = 2,955%

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

#### 29.55 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:

#### 29.55 = ^{29.55}/_{1}

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

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

#### This number is: 100.

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

^{29.55}/_{1} =

^{(29.55 × 100)}/_{(1 × 100)} =

^{2,955}/_{100}

## 3. Reduce (simplify) the fraction above: ^{2,955}/_{100}

(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}):

#### 2,955 = 3 × 5 × 197

#### 100 = 2^{2} × 5^{2}

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

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

#### GCF (3 × 5 × 197; 2^{2} × 5^{2}) = 5

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

^{2,955}/_{100} =

^{(3 × 5 × 197)}/_{(22 × 52)} =

^{((3 × 5 × 197) ÷ 5)} / _{((22 × 52) ÷ 5)} =

^{(3 × 197)}/_{(22 × 5)} =

^{591}/_{20}

## 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.

#### 591 ÷ 20 = 29, remainder = 11 =>

#### 591 = 29 × 20 + 11 =>

#### ^{591}/_{20} =

#### ^{(29 × 20 + 11)} / _{20} =

^{(29 × 20)} / _{20} + ^{11}/_{20} =

#### 29 + ^{11}/_{20} =

#### 29 ^{11}/_{20}

^{591}/_{20}: 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 4:

^{591}/_{20} = ^{(591 × 4)}/_{(20 × 4)} = ^{2,364}/_{80}

### Example 2. By expanding the fraction by 7:

^{591}/_{20} = ^{(591 × 7)}/_{(20 × 7)} = ^{4,137}/_{140}

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

#### ... to the initial fraction: ^{591}/_{20}