# Improper Fractions

\frac{7}{4}

*(seven-fourths or*

seven-quarters)

seven-quarters)

An Improper Fraction has a top number larger than (or equal to) the bottom number.

It is usually "**top-heavy**"

### More Examples:

See how the top number is bigger than (or equal to) the bottom number?

That makes it an Improper Fraction, (but there is nothing wrong about Improper Fractions).

## Three Types of Fractions

There are three types of fraction:

## Fractions

A Fraction (such as ^{7}/_{4}) has two numbers:

\frac{Numerator}{Denominator}

The top number (the Numerator) is the number of **parts we have**.

The bottom number (the Denominator) is the number of **parts the whole is divided into**.

### Example: ^{7}/_{4} means:

- We have
**7**parts - Each part is a
**quarter**(^{1}/_{4}) of a whole

So we can define the three types of fractions like this:

Examples:

^{1}/

_{3},

^{3}/

_{4},

^{2}/

_{7}

Examples:

^{4}/

_{3},

^{11}/

_{4},

^{7}/

_{7}

Examples: 1

^{1}/

_{3}, 2

^{1}/

_{4}, 16

^{2}/

_{5}

## Improper Fraction

So an improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator): it is **top-heavy**.

\frac{4}{4}

### Can be Equal

What about when the numerator equals the denominator? Such as \frac{4}{4} ?

Well it is the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction.

## Improper Fractions or Mixed Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 1\frac{3}{4} = \frac{7}{4}, as shown here:

1\frac{3}{4} | \frac{7}{4} | |

= |

## Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

- Divide the numerator by the denominator.
- Write down the whole number answer
- Then write down any remainder above the denominator.

### Example: Convert \frac{11}{4} to a mixed fraction.

Divide:

Write down the 2 and then write down the remainder (3) above the denominator (4).

Answer:

2 \frac{3}{4}

That example can be written like this:

### Example: Convert \frac{10}{3} to a mixed fraction.

Answer:

3 \frac{1}{3}

## Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

- Multiply the whole number part by the fraction's denominator.
- Add that to the numerator
- Then write the result on top of the denominator.

### Example: Convert 3\frac{2}{5} to an improper fraction.

Multiply the whole number part by the denominator:

Add that to the numerator:

Then write that result above the denominator:

\frac{17}{5}

We can do the numerator in one go:

### Example: Convert 2\frac{1}{9} to an improper fraction.

## Are Improper Fractions Bad ?

NO, they aren't bad!

For mathematics they are actually **better** than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: **should the two parts be added or multiplied?**

**?**

*is it:*

**Or****?**

But, for **everyday use**, people understand mixed fractions better.

Example: It is easier to say "I ate 2\frac{1}{4} sausages", than "I ate \frac{9}{4} sausages"

We Recommend:

- For Mathematics: Improper Fractions
- For Everyday Use: Mixed Fractions