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Answer :
To subtract the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex], first find a common denominator. The denominators here are 15 and 5. The least common multiple (LCM) of 15 and 5 is 15.
Next, rewrite [tex]\(\frac{2}{5}\)[/tex] with a denominator of 15. To do this, multiply both the numerator and the denominator by 3:
[tex]\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\][/tex]
Now, subtract the fractions with the common denominator:
[tex]\[
\frac{13}{15} - \frac{6}{15} = \frac{13 - 6}{15} = \frac{7}{15}
\][/tex]
The fraction [tex]\(\frac{7}{15}\)[/tex] is already in its simplest form because 7 and 15 have no common factors other than 1.
Therefore, the final answer is [tex]\(\frac{7}{15}\)[/tex].
Next, rewrite [tex]\(\frac{2}{5}\)[/tex] with a denominator of 15. To do this, multiply both the numerator and the denominator by 3:
[tex]\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\][/tex]
Now, subtract the fractions with the common denominator:
[tex]\[
\frac{13}{15} - \frac{6}{15} = \frac{13 - 6}{15} = \frac{7}{15}
\][/tex]
The fraction [tex]\(\frac{7}{15}\)[/tex] is already in its simplest form because 7 and 15 have no common factors other than 1.
Therefore, the final answer is [tex]\(\frac{7}{15}\)[/tex].
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