# Mixed Fractions

*(Also called " Mixed Numbers")*

1\frac{3}{4} |

(one and three-quarters) |

A Mixed Fraction is a
whole number
and a proper fraction
combined.

Such as 1\frac{3}{4}

## Examples

2\frac{3}{8} | 7\frac{1}{4} | 1\frac{14}{15} | 21\frac{4}{5} |

See how each example is made up of a whole number **and** a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).

## Names

We can give names to every part of a mixed fraction:

## Three Types of Fractions

There are three types of fraction:

## Mixed Fractions or Improper 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?**

Mixed Fraction: | What is: | 1 + 2\frac{1}{4} ? | |||
---|---|---|---|---|---|

it may be: | 1 + 2 + \frac{1}{4} | = 3\frac{1}{4} | |||

Or it may be: |
1 + 2 × \frac{1}{4} | = 1\frac{1}{2} | |||

Improper Fraction: | What is: | 1 + \frac{9}{4} ? | |||

It is: | \frac{4}{4} + \frac{9}{4} = \frac{13}{4} |

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