Answer :
To divide the fractions [tex]\(\frac{13}{15}\)[/tex] by [tex]\(\frac{7}{10}\)[/tex], we can follow these steps:
1. Find the Reciprocal of the Divisor:
The divisor here is [tex]\(\frac{7}{10}\)[/tex]. To divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex].
2. Perform the Multiplication:
Multiply the first fraction [tex]\(\frac{13}{15}\)[/tex] by the reciprocal of the second fraction [tex]\(\frac{10}{7}\)[/tex]:
[tex]\[
\frac{13}{15} \times \frac{10}{7} = \frac{13 \times 10}{15 \times 7} = \frac{130}{105}
\][/tex]
3. Simplify the Resulting Fraction:
To simplify [tex]\(\frac{130}{105}\)[/tex], we need to find the greatest common divisor (GCD) of 130 and 105. The GCD is 5. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}
\][/tex]
So, the division [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] in simplest form is [tex]\(\frac{26}{21}\)[/tex].
1. Find the Reciprocal of the Divisor:
The divisor here is [tex]\(\frac{7}{10}\)[/tex]. To divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex].
2. Perform the Multiplication:
Multiply the first fraction [tex]\(\frac{13}{15}\)[/tex] by the reciprocal of the second fraction [tex]\(\frac{10}{7}\)[/tex]:
[tex]\[
\frac{13}{15} \times \frac{10}{7} = \frac{13 \times 10}{15 \times 7} = \frac{130}{105}
\][/tex]
3. Simplify the Resulting Fraction:
To simplify [tex]\(\frac{130}{105}\)[/tex], we need to find the greatest common divisor (GCD) of 130 and 105. The GCD is 5. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}
\][/tex]
So, the division [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] in simplest form is [tex]\(\frac{26}{21}\)[/tex].
