## 1. Write the number as a percentage.

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

#### 0.7 =

#### 0.7 × ^{100}/_{100} =

^{(0.7 × 100)}/_{100} =

#### ^{70}/_{100} =

#### 70%

#### In other words:

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

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

#### 0.7 = 70%

## 2. Write the number as a proper fraction.

#### 0.7 can be written as a proper fraction.

#### (The numerator is smaller than the denominator).

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

#### 0.7 = ^{0.7}/_{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)

^{0.7}/_{1} =

^{(0.7 × 10)}/_{(1 × 10)} =

^{7}/_{10}

## 3. Reduce (simplify) the fraction above: ^{7}/_{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).

#### 7 is a prime number, it cannot be factored into other prime factors

#### 10 = 2 × 5

### 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; 2 × 5) = 1

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

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

^{7}/_{10}: 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 2:

^{7}/_{10} = ^{(7 × 2)}/_{(10 × 2)} = ^{14}/_{20}

### Example 2. By expanding the fraction by 5:

^{7}/_{10} = ^{(7 × 5)}/_{(10 × 5)} = ^{35}/_{50}

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

#### ... to the initial fraction: ^{7}/_{10}