### Learning Outcomes

- Convert between improper fractions and mixed numbers

In an earlier example, we converted the improper fraction [latex]{\Large\frac{11}{6}}[/latex] to the mixed number [latex]1{\Large\frac{5}{6}}[/latex] using fraction circles. We did this by grouping six sixths together to make a whole; then we looked to see how many of the [latex]11[/latex] pieces were left. We saw that [latex]{\Large\frac{11}{6}}[/latex] made one whole group of six sixths plus five more sixths, showing that [latex]{\Large\frac{11}{6}}=1{\Large\frac{5}{6}}[/latex].

The division expression [latex]{\Large\frac{11}{6}}[/latex] (which can also be written as [latex]6\overline{)11}[/latex] ) tells us to find how many groups of [latex]6[/latex] are in [latex]11[/latex]. To convert an improper fraction to a mixed number without fraction circles, we divide.

### Example

Convert [latex]{\Large\frac{11}{6}}[/latex] to a mixed number.

Solution:

[latex]{\Large\frac{11}{6}}[/latex] | |

Divide the denominator into the numerator. | Remember [latex]{\Large\frac{11}{6}}[/latex] means [latex]11\div 6[/latex] |

Identify the quotient, remainder and divisor. | |

Write the mixed number as [latex]\text{quotient }({\Large\frac{\text{remainder}}{\text{divisor}}})[/latex] . | [latex]1{\Large\frac{5}{6}}[/latex] |

So, [latex]{\Large\frac{11}{6}}=1{\Large\frac{5}{6}}[/latex] |

### Try it

### Convert an improper fraction to a mixed number.

- Divide the denominator into the numerator.
- Identify the quotient, remainder, and divisor.
- Write the mixed number as quotient [latex]{\Large\frac{\text{remainder}}{\text{divisor}}}[/latex] .

### Example

Convert the improper fraction [latex]{\Large\frac{33}{8}}[/latex] to a mixed number.

### try it

Now you can watch worked examples of how to convert an improper fraction to a mixed number in the following video.

In an earlier example, we changed [latex]1{\Large\frac{4}{5}}[/latex] to an improper fraction by first seeing that the whole is a set of five fifths. So we had five fifths and four more fifths.

[latex]{\Large\frac{5}{5}}+{\Large\frac{4}{5}}={\Large\frac{9}{5}}[/latex]

Where did the nine come from? There are nine fifths—one whole (five fifths) plus four fifths. Let us use this idea to see how to convert a mixed number to an improper fraction.

### Example

Convert the mixed number [latex]4{\Large\frac{2}{3}}[/latex] to an improper fraction.

### try it

### Convert a mixed number to an improper fraction.

- Multiply the whole number by the denominator.
- Add the numerator to the product found in Step 1.
- Write the final sum over the original denominator.

### Example

Convert the mixed number [latex]10{\Large\frac{2}{7}}[/latex] to an improper fraction.

### Try it

In the following video we show more example of how to convert a mixed number to an improper fraction.