Answer :
To divide fractions, you follow these steps:
1. Write the Problem: Start with the division of two fractions: [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex].
2. Find the Reciprocal of the Second Fraction: The reciprocal of a fraction is simply flipping the numerator and the denominator. So, the reciprocal of [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex].
3. Change Division to Multiplication: When you divide by a fraction, it's the same as multiplying by its reciprocal. Therefore, [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] becomes [tex]\(\frac{13}{15} \times \frac{10}{7}\)[/tex].
4. Multiply the Fractions: Multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
[tex]\[
\frac{13 \times 10}{15 \times 7} = \frac{130}{105}
\][/tex]
5. Simplify the Fraction: To simplify [tex]\(\frac{130}{105}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator, which is 5:
[tex]\[
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}
\][/tex]
So, the result of dividing [tex]\(\frac{13}{15}\)[/tex] by [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{26}{21}\)[/tex] or [tex]\(1 \frac{5}{21}\)[/tex] if you prefer a mixed number.
This fraction [tex]\(\frac{26}{21}\)[/tex] is approximately equal to 1.238, which is a decimal representation of the answer.
1. Write the Problem: Start with the division of two fractions: [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex].
2. Find the Reciprocal of the Second Fraction: The reciprocal of a fraction is simply flipping the numerator and the denominator. So, the reciprocal of [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{10}{7}\)[/tex].
3. Change Division to Multiplication: When you divide by a fraction, it's the same as multiplying by its reciprocal. Therefore, [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] becomes [tex]\(\frac{13}{15} \times \frac{10}{7}\)[/tex].
4. Multiply the Fractions: Multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
[tex]\[
\frac{13 \times 10}{15 \times 7} = \frac{130}{105}
\][/tex]
5. Simplify the Fraction: To simplify [tex]\(\frac{130}{105}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator, which is 5:
[tex]\[
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}
\][/tex]
So, the result of dividing [tex]\(\frac{13}{15}\)[/tex] by [tex]\(\frac{7}{10}\)[/tex] is [tex]\(\frac{26}{21}\)[/tex] or [tex]\(1 \frac{5}{21}\)[/tex] if you prefer a mixed number.
This fraction [tex]\(\frac{26}{21}\)[/tex] is approximately equal to 1.238, which is a decimal representation of the answer.
