To solve the problem of dividing two fractions and then reducing to the lowest terms, follow this step-by-step method:
Given:
[tex]\[
\frac{7}{11} \div \frac{2}{3}
\][/tex]
1. Division of Fractions: To divide one fraction by another, you multiply by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by switching its numerator and denominator.
The reciprocal of [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{3}{2}\)[/tex].
2. Multiplying by the Reciprocal:
Now, multiply [tex]\(\frac{7}{11}\)[/tex] by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
\frac{7}{11} \times \frac{3}{2} = \frac{7 \times 3}{11 \times 2} = \frac{21}{22}
\][/tex]
3. Simplify the Fraction: The fraction [tex]\(\frac{21}{22}\)[/tex] should be simplified if possible. Simplification is done by finding the Greatest Common Divisor (GCD) of the numerator and the denominator and then dividing both by this GCD.
In this case, the GCD of 21 and 22 is 1 (as 21 and 22 are co-primes, meaning they have no common divisors other than 1).
Thus, the fraction [tex]\(\frac{21}{22}\)[/tex] is already in its simplest form.
Therefore, the result of dividing [tex]\(\frac{7}{11}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex] and simplifying is:
[tex]\[
\frac{21}{22}
\][/tex]
