Denominators and mixed numbers, converting fractions to decimals, and more.

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## What is a Fraction?

A fraction (from Latin fractus, “broken”) represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (e.g. 1/2, 2/5, 3/4) consists of an integer numerator displayed above a line (or before a slash mark) and an integer denominator displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common (such as 21/9), including compound fractions (such as 2 1/2).

## Types of Fractions

A fraction (from Latin fractus, “broken”) represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: 1/2, 2/5, 3/4) consists of an integer numerator displayed above a line (or before a slash) and a non-zero integer denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed fractions.

### Proper Fractions

A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number).

For example 1/2, 3/4, 4/5 and 5/6 are proper fractions.

Proper fractions are sometimes also called top heavy fractions.

### Improper Fractions

A fraction (from Latin fractus, “broken”) represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for instance, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: 1/2, 2/3, 3/4) consists of an integer numerator displayed above a line (or before a slash) and an integer denominator displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions (examples: 1 1/2 or 2 3/4), complex fractions (example: 1 + 1/2), and mixed numerals or mixed fractions (examples: 3 + 1/4 or 2_3/4).

There are three types of fractions: proper fractions, improper fractions and mixed numbers.

Proper Fraction

A proper fraction is a fraction where the numerator is less than the denominator.

For example 1/3 is a proper fraction because the numerator (1) is less than the denominator (3).

1 3

Proper Fraction= −−−−−−–>

3

Improper Fraction

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

For example 5/4 is an improper fraction because the numerator (5) is greater than the denominator (4).

5 4

Improper Fraction= −−−−−> OR it can be written as −→ OR it can be written as 1_1/4

4

Remember: An improper fraction can be expressed as a mixed number.

### Mixed Fractions

A mixed fraction (also called a mixed number) is a whole number plus a proper fraction. It is written in the form a b/c.

For example, 3 1/2, 7/4, and 2 3/8 are all mixed fractions. The whole number is written first, followed by a space, followed by the fractional part.

To convert a mixed fraction to an improper fraction, multiply the whole number portion by the denominator of the fractional part, and add this product to the numerator of the fractional part. In other words:

a b/c = (ac + b)/c

## How to Convert a Fraction to a Decimal

To convert a fraction to a decimal, divide the numerator by the denominator.

For example, if someone plugs the fraction ¾ into a calculator, they would get the decimal .75 on the screen. And if someone plugs in the fraction 2/5, they would get .4 displayed on the screen.

## How to Convert a Decimal to a Fraction

Converting a decimal to a fraction is a two-step process. The first step is to find the place value of the decimal point. The second step is to count the number of places to the right of the decimal point. This will be the denominator of your fraction. The numerator will be the number that is currently in that place.

## How to Simplify a Fraction

When you simplify a fraction, you make it easier to work with. You might need to do this to add or subtract fractions, or to compare fractions. To simplify a fraction, divide both the top (numerator) and bottom (denominator) by the same number until there is nothing left to divide by. This number is called the Greatest Common Factor (GCF).