Learning Outcomes
- Convert mixed numbers to improper fractions
- Convert improper fractions to 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.