Answer :

To add the fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{13}{15}\)[/tex], follow these steps:

1. Find a Common Denominator:
The denominators are 5 and 15. The least common multiple (LCM) of 5 and 15 is 15. So, we’ll use 15 as the common denominator.

2. Convert Each Fraction to Have the Common Denominator:
- For [tex]\(\frac{3}{5}\)[/tex], convert it to a fraction with 15 as the denominator. You can do this by multiplying both the numerator and the denominator by 3:
[tex]\[
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
\][/tex]

- The fraction [tex]\(\frac{13}{15}\)[/tex] already has 15 as the denominator, so it stays the same:
[tex]\[
\frac{13}{15} = \frac{13}{15}
\][/tex]

3. Add the Fractions:
Now that both fractions have the same denominator, you can simply add their numerators:
[tex]\[
\frac{9}{15} + \frac{13}{15} = \frac{9 + 13}{15} = \frac{22}{15}
\][/tex]

4. Convert to a Mixed Number (if needed):
Since [tex]\(\frac{22}{15}\)[/tex] is an improper fraction, you can also express it as a mixed number:
- Divide 22 by 15 to get 1 with a remainder of 7. So, [tex]\(\frac{22}{15}\)[/tex] can be written as:
[tex]\[
1 \frac{7}{15}
\][/tex]

Therefore, [tex]\(\frac{3}{5} + \frac{13}{15} = \frac{22}{15}\)[/tex] or as a mixed number, [tex]\(1 \frac{7}{15}\)[/tex].

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