College

Divide.

\[ \frac{13}{15} \div \frac{1}{5} \]

\[ \frac{13}{15} \div \frac{1}{5} = \square \]

(Type a whole number or a simplified fraction.)

Answer :

To solve the problem of adding the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{1}{5}\)[/tex], you need a common denominator. Here’s the step-by-step process:

1. Find the Least Common Denominator (LCD):
- The denominators are 15 and 5.
- The least common multiple of 15 and 5 is 15, so 15 will be our common denominator.

2. Rewrite each fraction with the common denominator:
- The fraction [tex]\(\frac{13}{15}\)[/tex] already has the denominator 15, so it stays the same: [tex]\(\frac{13}{15}\)[/tex].
- To rewrite [tex]\(\frac{1}{5}\)[/tex] with the denominator 15, we multiply both the numerator and denominator by 3:
[tex]\[
\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}
\][/tex]

3. Add the fractions:
- Now that both fractions have the same denominator, you can add them:
[tex]\[
\frac{13}{15} + \frac{3}{15} = \frac{13 + 3}{15} = \frac{16}{15}
\][/tex]

4. Simplify the fraction if necessary:
- The fraction [tex]\(\frac{16}{15}\)[/tex] is already in its simplest form because 16 and 15 have no common factors other than 1.

Therefore, the result of [tex]\(\frac{13}{15} + \frac{1}{5}\)[/tex] is [tex]\(\boxed{\frac{16}{15}}\)[/tex].

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