WeBWorK using host: https://webwork.pcc.edu, format: simple, seed: 84, course: orcca

Here are some practice exercises involving addition with mixed numbers, where the fractions have common denominators. The expectation is that readers can make these calculations here without a calculator.

Add: $3\,\frac{1}{8}+2\,\frac{5}{8}\text{.}$

Add: $2\,\frac{3}{10}+6\,\frac{9}{10}\text{.}$

Solution

First, we add the whole numbers: $3+2=5\text{.}$ Then, we add the fractions: $\frac{1}{8}+\frac{5}{8}=\frac{6}{8}\text{.}$
The last step is to simplify, which means we need to reduce the fraction, if possible.
The simplification step, including the whole number, can be shown as follows:
$5\,\frac{6}{8}=5\,\frac{3}{4}\text{.}$
Therefore, $3\,\frac{1}{8}+2\,\frac{5}{8}=5\,\frac{3}{4}\text{.}$

First, we add the whole numbers: $2+6=8\text{.}$ Then, we add the fractions: $\frac{3}{10}+\frac{9}{10}=\frac{12}{10}\text{.}$
The last step is to simplify, which means we need to reduce the fraction, if possible. However, it also means that if the fraction turns out to be improper, we must convert it to a mixed number and then combine the whole number part to the result of adding the original whole numbers.
The simplification steps, including the whole numbers, can be shown as follows:
$\begin{aligned} 8\,\frac{12}{10}\amp=8\,\frac{6}{5}\\ \amp=8+1\,\frac{1}{5}\\ \amp=9\,\frac{1}{5}\text{.} \end{aligned}$
Therefore, $2\,\frac{3}{10}+6\,\frac{9}{10}=9\,\frac{1}{5}\text{.}$