Answer :
To divide two fractions, you need to multiply the first fraction by the reciprocal of the second fraction. Let's solve the problem step-by-step:
1. Identify the fractions:
- The problem is asking you to divide [tex]\(\frac{13}{15}\)[/tex] by [tex]\(\frac{7}{10}\)[/tex].
2. Find the reciprocal of the second fraction:
- The reciprocal of [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex]. You simply swap the numerator and the denominator to find the reciprocal.
3. Multiply the fractions:
- Now, you multiply the first fraction by the reciprocal of the second fraction:
[tex]\[
\frac{13}{15} \times \frac{10}{7}
\][/tex]
- Multiply the numerators: [tex]\(13 \times 10 = 130\)[/tex].
- Multiply the denominators: [tex]\(15 \times 7 = 105\)[/tex].
4. Write the result as a fraction:
- The result of multiplying the fractions is [tex]\(\frac{130}{105}\)[/tex].
5. Simplify the fraction:
- To simplify [tex]\(\frac{130}{105}\)[/tex], find the greatest common divisor (GCD) of 130 and 105, which is 5.
- Divide both the numerator and the denominator by their GCD:
- [tex]\(130 \div 5 = 26\)[/tex].
- [tex]\(105 \div 5 = 21\)[/tex].
6. Write the simplest form:
- The fraction in simplest form is [tex]\(\frac{26}{21}\)[/tex].
So, [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] simplifies to [tex]\(\frac{26}{21}\)[/tex].
1. Identify the fractions:
- The problem is asking you to divide [tex]\(\frac{13}{15}\)[/tex] by [tex]\(\frac{7}{10}\)[/tex].
2. Find the reciprocal of the second fraction:
- The reciprocal of [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex]. You simply swap the numerator and the denominator to find the reciprocal.
3. Multiply the fractions:
- Now, you multiply the first fraction by the reciprocal of the second fraction:
[tex]\[
\frac{13}{15} \times \frac{10}{7}
\][/tex]
- Multiply the numerators: [tex]\(13 \times 10 = 130\)[/tex].
- Multiply the denominators: [tex]\(15 \times 7 = 105\)[/tex].
4. Write the result as a fraction:
- The result of multiplying the fractions is [tex]\(\frac{130}{105}\)[/tex].
5. Simplify the fraction:
- To simplify [tex]\(\frac{130}{105}\)[/tex], find the greatest common divisor (GCD) of 130 and 105, which is 5.
- Divide both the numerator and the denominator by their GCD:
- [tex]\(130 \div 5 = 26\)[/tex].
- [tex]\(105 \div 5 = 21\)[/tex].
6. Write the simplest form:
- The fraction in simplest form is [tex]\(\frac{26}{21}\)[/tex].
So, [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] simplifies to [tex]\(\frac{26}{21}\)[/tex].
