Answer :

To solve the problem of dividing [tex]\(\frac{13}{15}\)[/tex] by [tex]\(\frac{7}{10}\)[/tex], follow these steps:

1. Understand Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator. So, [tex]\(\frac{7}{10}\)[/tex] becomes [tex]\(\frac{10}{7}\)[/tex].

2. Rewrite the Problem as Multiplication:
[tex]\[
\frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7}
\][/tex]

3. Multiply the Fractions: Multiply the numerators and the denominators.

[tex]\[
\text{Numerator: } 13 \times 10 = 130
\][/tex]
[tex]\[
\text{Denominator: } 15 \times 7 = 105
\][/tex]

So, the result of the multiplication is:
[tex]\[
\frac{130}{105}
\][/tex]

4. Simplify the Fraction: To simplify [tex]\(\frac{130}{105}\)[/tex], find the greatest common divisor (GCD) of 130 and 105. The GCD of 130 and 105 is 5.

5. Divide Both the Numerator and Denominator by the GCD:
[tex]\[
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}
\][/tex]

Thus, the division [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] simplifies to [tex]\(\frac{26}{21}\)[/tex]. This is the simplest form of the fraction.

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Rewritten by : Barada