Answer :
To solve the division of two fractions, follow these steps:
1. Identify the fractions: The fractions given in the problem are [tex]\(\frac{9}{15}\)[/tex] and [tex]\(\frac{27}{30}\)[/tex].
2. Reciprocal of the second fraction: When dividing fractions, take the reciprocal (flip) of the second fraction and multiply:
[tex]\[
\text{Reciprocal of } \frac{27}{30} \text{ is } \frac{30}{27}.
\][/tex]
3. Multiply the fractions: Multiply the first fraction by the reciprocal of the second fraction:
[tex]\[
\frac{9}{15} \times \frac{30}{27}.
\][/tex]
4. Multiply the numerators and denominators:
[tex]\[
\text{Numerator: } 9 \times 30 = 270,
\][/tex]
[tex]\[
\text{Denominator: } 15 \times 27 = 405.
\][/tex]
So, we get [tex]\(\frac{270}{405}\)[/tex].
5. Simplify the fraction: To simplify [tex]\(\frac{270}{405}\)[/tex], find the greatest common divisor (GCD) of 270 and 405, which is 135.
Divide both the numerator and denominator by 135:
[tex]\[
\frac{270 \div 135}{405 \div 135} = \frac{2}{3}.
\][/tex]
Thus, the answer to the problem [tex]\(\frac{9}{15} \div \frac{27}{30}\)[/tex] is [tex]\(\frac{2}{3}\)[/tex], which corresponds to option A.
1. Identify the fractions: The fractions given in the problem are [tex]\(\frac{9}{15}\)[/tex] and [tex]\(\frac{27}{30}\)[/tex].
2. Reciprocal of the second fraction: When dividing fractions, take the reciprocal (flip) of the second fraction and multiply:
[tex]\[
\text{Reciprocal of } \frac{27}{30} \text{ is } \frac{30}{27}.
\][/tex]
3. Multiply the fractions: Multiply the first fraction by the reciprocal of the second fraction:
[tex]\[
\frac{9}{15} \times \frac{30}{27}.
\][/tex]
4. Multiply the numerators and denominators:
[tex]\[
\text{Numerator: } 9 \times 30 = 270,
\][/tex]
[tex]\[
\text{Denominator: } 15 \times 27 = 405.
\][/tex]
So, we get [tex]\(\frac{270}{405}\)[/tex].
5. Simplify the fraction: To simplify [tex]\(\frac{270}{405}\)[/tex], find the greatest common divisor (GCD) of 270 and 405, which is 135.
Divide both the numerator and denominator by 135:
[tex]\[
\frac{270 \div 135}{405 \div 135} = \frac{2}{3}.
\][/tex]
Thus, the answer to the problem [tex]\(\frac{9}{15} \div \frac{27}{30}\)[/tex] is [tex]\(\frac{2}{3}\)[/tex], which corresponds to option A.
