# Classification of Fractions

### Proper fractions

Proper fractions are those whose numerator is less than the denominator. Its overall value is between zero and one.

### Improper Fractions

Improper fractions are those whose numerator is greater than the denominator. Its overall value is greater than one.

#### Mixed Number

*The mixed number or mixed fraction* is composed of a

**integer part**and

**fraction**.

To convert a **mixed number** to** an improper fraction,** the numerator becomes the sum** of the product** of the integer and the denominator plus the numerator. The denominator remains the same.

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient then becomes the integer of the mixed number and the remainder becomes the numerator of the fraction. The denominator remains the same.

### Decimal fractions

The** decimal fractions** have as a denominator a** power of 10**.

### Equivalent Fractions

Two fractions are equivalent when the product** of its extremes is**** equal to the product of its middles**.

**a** and **d** are the extremes; **b** and **c**, are the middles.

Determine whether the follwing fractions are equivalent:

4 · 12 = 6 · 8 48 = 48 Yes

If a fraction is multiplied by a fraction of an integer (a whole fraction) not including zero, the result is equivalent to the original fraction.

In the first case, it is called extended or amplified.

### Simplifying fractions

**Simplifying or reducing a fraction** is transforming it into a simpler,** equivalent fraction**.

To simplify a fraction,** divide the numerator and the denominator** by the same number.

In order to determine what number to divide by, find the first prime numbers of both the numerator and denominator: 2, 3, 5, 7, ... In other words, try to divide** the numerator and denominator** by a number divisible by both.

The process is repeated until there is no more common divisors.

If the terms of the** fraction** end up in** zeros**, begin by removing the final common zeros of the numerator and denominator.

If the number for which the numerator and denominator are divided by is the greatest common divisor of both, an irreducible fraction is reached.

### Irreducible fractions

The** irreducible fractions** are those that cannot be** simplified** any further. This happens when the numerator and denominator are both coprime.