A mixed number, also called a mixed fraction, has both a whole number and a fractional part. The fractional part may be a common fraction, or it may be in decimal form.
Converting mixed numbers to improper fractions
Although it is usually easier to understand mixed numbers in everyday situations, when performing fraction operations, it is important to be able to convert mixed numbers to an improper fraction because it makes calculations easier in many situations. To convert mixed fractions to improper fractions, use the following steps:
- Multiply the denominator of the fraction by the whole number. If the mixed number contains decimals, convert the decimals to a fraction first
- Add the numerator of the fraction to the product of the denominator and the whole number
- Write the result of the above operations over the denominator of the fraction
- Simplify the improper fraction if necessary; if the fraction in the mixed number is already in simplest form, simplification won't be necessary
Convert 3 to an improper fraction:
First, we multiply the whole number by the denominator of the fraction:
3 × 8 = 24
Then we add the numerator to this result:
24 + 7 = 31
Then we write the result over the denominator of the fraction:
Because the fraction is already in simplest form, the improper fraction is too. If for example, we had the equivalent fraction , we would've gotten:
Since 62 and 16 share a factor of 2, we would then simplify by factoring out the 2 to get what we did before, .
One way to visualize the process above is writing a letter "C" around the mixed number to remember the order that the operations should be performed in:
We read this image clockwise starting from the bottom of the C as: 8 × 3 + 7 = 31, where the end of the C shows us where to write the result (the numerator), and the denominator stays the same.
To understand why this method works, think about fractions. Since fractions must have the same denominator to be added or subtracted, multiplying the denominator by the whole number effectively converts the whole number into its fraction form with the same denominator as the original fraction, allowing us to add the whole number and the fraction to form an improper fraction.
Referring to our previous example, the fraction , so the whole number portion, 3, can be read as . So in the mixed number above, we'd have .
See also decimal mixed number.