Sure! Let's go through the steps to find the sum of two fractions, \(\frac{1}{5}\) and \(\frac{7}{10}\), in detail.
### Step 1: Choose the lowest common denominator (LCD).
The denominators of the two given fractions are 5 and 10. The lowest common denominator (LCD) for 5 and 10 is 10, as it is the smallest number that both 5 and 10 can divide into without leaving a remainder.
### Step 2: Rewrite each fraction with the common denominator.
Now, we need to rewrite each fraction so that they have the common denominator of 10.
- For \(\frac{1}{5}\):
- Multiply both the numerator and the denominator by 2 to get the denominator to 10.
- Thus, \(\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}\).
- For \(\frac{7}{10}\):
- The denominator is already 10, so this fraction does not need to be changed.
- Thus, \(\frac{7}{10} = \frac{7}{10}\).
### Step 3: Sum the fractions.
Now, add the fractions \(\frac{2}{10}\) and \(\frac{7}{10}\) since they have the same denominator.
[tex]\[
\frac{2}{10} + \frac{7}{10} = \frac{2 + 7}{10} = \frac{9}{10}
\][/tex]
### Final Answer:
The equivalent fractions with a common denominator are [tex]\(\frac{2}{10}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex]. The sum of these fractions is [tex]\(\frac{9}{10}\)[/tex].
