Adding and subtracting mixed numbers
Add or subtract the whole numbers and the fractions separately, then combine the results
We can add and subtract mixed numbers, each of which is the sum of a whole number and a fraction.
When we need to add or subtract mixed numbers, we deal with the whole numbers separately from the fractions, and we find a common denominator for the fractions.
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Examples of finding the sum and difference of mixed numbers
Example
Find the sum.
???6\frac37+2\frac14???
First, we’ll separate the whole numbers from the fractions.
???\left(6+2\right)+\left(\frac37+\frac14\right)???
Next, we’ll find a common denominator for the fractions.
???\left(6+2\right)+\left[\frac37\left(\frac44\right)+\frac14\left(\frac77\right)\right]???
???\left(6+2\right)+\left(\frac{12}{28}+\frac{7}{28}\right)???
Now we’ll add the whole numbers and the fractions separately.
???8+\frac{19}{28}???
As a mixed number, the answer is
???8\frac{19}{28}???
If we want to convert this to an improper fraction, we’ll take the following steps:
???8\frac{19}{28}=\frac{(28\times8)+19}{28}???
???8\frac{19}{28}=\frac{224+19}{28}???
???8\frac{19}{28}=\frac{243}{28}???
Let’s try an example of subtraction of mixed numbers.
When we need to add or subtract mixed numbers, we deal with the whole numbers separately from the fractions, and we find a common denominator for the fractions.
Example
Find the difference.
???6\frac37-2\frac14???
First, we’ll separate the whole numbers from the fractions.
???\left(6-2\right)+\left(\frac37-\frac14\right)???
Next, we’ll find a common denominator for the fractions.
???\left(6-2\right)+\left[\frac37\left(\frac44\right)-\frac14\left(\frac77\right)\right]???
???\left(6-2\right)+\left(\frac{12}{28}-\frac{7}{28}\right)???
Now we’ll subtract the whole numbers and the fractions separately.
???4+\frac{5}{28}???
As a mixed number, the answer is
???4\frac{5}{28}???
If we want to convert this to an improper fraction, we’ll take the following steps:
???4\frac{5}{28}=\frac{(28\times4)+5}{28}???
???4\frac{5}{28}=\frac{112+5}{28}???
???4\frac{5}{28}=\frac{117}{28}???
