Converting Between Improper Fractions and Mixed Numbers
One way to visualize a fraction is as parts of a whole, as in [latex]\frac{5}{12}[/latex] of a pizza. But when the numerator is larger than the denominator, as in [latex]\frac{23}{12}[/latex], then the idea of parts of a whole seems not to make sense.
Such a fraction is an improper fraction. That kind of fraction could be written as an integer plus a fraction, which is a mixed number. The fraction [latex]\frac{23}{12}[/latex] rewritten as a mixed number would be [latex]1\frac{11}{12}[/latex]. Arithmetically, [latex]1\frac{11}{12}[/latex] is equivalent to [latex]1 + \frac{11}{12}[/latex], which is read as “one and 11 twelfths.”
Improper fractions can be rewritten as mixed numbers using division and remainders.
How to: Convert Between Improper Fractions and Mixed Numbers
To find the mixed number representation of an improper fraction, divide the numerator by the denominator. The quotient is the integer part, and the remainder becomes the numerator of the remaining fraction.
Convert [latex]{\Large\frac{11}{6}}[/latex] to a mixed number.
Rewrite [latex]\frac{48}{13}[/latex] as a mixed number.
Similarly, we can convert a mixed number into an improper fraction.
How to: Convert Between Mixed Numbers and Improper Fractions
To convert a mixed number to an improper fraction, first convert the whole number part to a fraction by writing the whole number as itself divided by [latex]1[/latex], and then add the two fractions.
Alternately, we can multiply the whole number part and the denominator of the fractional part. Next, add that product to the numerator. Finally, express the number as that product divided by the denominator.
Convert the mixed number [latex]4{\Large\frac{2}{3}}[/latex] to an improper fraction.
Rewrite [latex]5\frac{4}{9}[/latex] as an improper fraction.
Desmos can be used to convert from a mixed number to an improper fraction. To do so, we use the idea that a mixed number, such as [latex]5\frac{6}{11}[/latex], is another way to represent [latex]5+\frac{6}{11}[/latex].
If [latex]5+\frac{6}{11}[/latex] is entered in Desmos, the result is the decimal form of the number. However, clicking the fraction button to the left will convert the decimal to an improper fraction, [latex]\frac{61}{11}[/latex].
As an added bonus, Desmos will automatically reduce the fraction to lowest terms. For more on how to use Desmos to convert an improper fraction to a mixed number, watch this video.
You can view the transcript for “Converting Improper Fractions to Mixed Number on the Desmos Scientific Calculator” here (opens in new window).