Certainly! Let's solve the problem of adding the two fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex] step-by-step.
### Step 1: Identify the Fractions
We have two fractions:
[tex]\[
\frac{3}{5} \quad \text{and} \quad \frac{7}{10}
\][/tex]
### Step 2: Find a Common Denominator
To add these fractions, we need a common denominator. The denominators are 5 and 10. The least common multiple (LCM) of 5 and 10 is 10.
### Step 3: Convert Fractions to Equivalent Fractions with a Common Denominator
We convert each fraction to have the common denominator of 10.
For [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
\][/tex]
For [tex]\(\frac{7}{10}\)[/tex]:
This fraction already has the common denominator, so it remains:
[tex]\[
\frac{7}{10}
\][/tex]
### Step 4: Add the Numerators
Now that both fractions have the same denominator, we can add the numerators:
[tex]\[
\frac{6}{10} + \frac{7}{10} = \frac{6 + 7}{10} = \frac{13}{10}
\][/tex]
### Step 5: Simplify the Result (if necessary)
The resulting fraction is [tex]\(\frac{13}{10}\)[/tex], which is already in its simplest form. The GCD of 13 and 10 is 1, so no further simplification is needed.
### Final Result
The sum of [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex] is:
[tex]\[
\frac{13}{10}
\][/tex]
We can also express this as a mixed number:
[tex]\[
\frac{13}{10} = 1 \frac{3}{10}.
\][/tex]
There you have it! The solution to [tex]\(\frac{3}{5} + \frac{7}{10}\)[/tex] is [tex]\(\frac{13}{10}\)[/tex] or [tex]\(1 \frac{3}{10}\)[/tex].
