## 1. Write the number as a percentage.

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

#### 1.19 =

#### 1.19 × ^{100}/_{100} =

^{(1.19 × 100)}/_{100} =

#### ^{119}/_{100} =

#### 119%

#### In other words:

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

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

#### 1.19 = 119%

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

#### 1.19 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:

#### 1.19 = ^{1.19}/_{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)

^{1.19}/_{1} =

^{(1.19 × 100)}/_{(1 × 100)} =

^{119}/_{100}

## 3. Reduce (simplify) the fraction above: ^{119}/_{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}):

#### 119 = 7 × 17

#### 100 = 2^{2} × 5^{2}

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

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

#### But, the numerator and the denominator have no common factors.

#### GCF (7 × 17; 2^{2} × 5^{2}) = 1

### The numerator and the denominator are coprime numbers (no common prime factors, GCF = 1).

So, the fraction cannot be reduced (simplified): irreducible fraction.

## 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.

#### 119 ÷ 100 = 1, remainder = 19 =>

#### 119 = 1 × 100 + 19 =>

#### ^{119}/_{100} =

#### ^{(1 × 100 + 19)} / _{100} =

^{(1 × 100)} / _{100} + ^{19}/_{100} =

#### 1 + ^{19}/_{100} =

#### 1 ^{19}/_{100}

^{119}/_{100}: 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:

^{119}/_{100} = ^{(119 × 5)}/_{(100 × 5)} = ^{595}/_{500}

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

^{119}/_{100} = ^{(119 × 7)}/_{(100 × 7)} = ^{833}/_{700}

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

#### ... to the initial fraction: ^{119}/_{100}