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Answer :
To find the quotient of the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex], you need to divide the first fraction by the second fraction. Here are the steps to follow:
1. Understand Division of Fractions:
To divide by a fraction, multiply by its reciprocal. The reciprocal of [tex]\(\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
2. Multiply the Fractions:
Multiply [tex]\(\frac{3}{4}\)[/tex] by [tex]\(\frac{6}{5}\)[/tex]:
[tex]\[
\frac{3}{4} \times \frac{6}{5} = \frac{3 \times 6}{4 \times 5} = \frac{18}{20}
\][/tex]
3. Simplify the Result:
To simplify [tex]\(\frac{18}{20}\)[/tex], look for the greatest common divisor (GCD) of 18 and 20, which is 2.
4. Divide Both Numerator and Denominator by the GCD:
[tex]\[
\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
So, the quotient of [tex]\(\frac{3}{4} \div \frac{5}{6}\)[/tex] is [tex]\(\frac{9}{10}\)[/tex]. The correct choice from the provided options is [tex]\(\frac{9}{10}\)[/tex].
1. Understand Division of Fractions:
To divide by a fraction, multiply by its reciprocal. The reciprocal of [tex]\(\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
2. Multiply the Fractions:
Multiply [tex]\(\frac{3}{4}\)[/tex] by [tex]\(\frac{6}{5}\)[/tex]:
[tex]\[
\frac{3}{4} \times \frac{6}{5} = \frac{3 \times 6}{4 \times 5} = \frac{18}{20}
\][/tex]
3. Simplify the Result:
To simplify [tex]\(\frac{18}{20}\)[/tex], look for the greatest common divisor (GCD) of 18 and 20, which is 2.
4. Divide Both Numerator and Denominator by the GCD:
[tex]\[
\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
So, the quotient of [tex]\(\frac{3}{4} \div \frac{5}{6}\)[/tex] is [tex]\(\frac{9}{10}\)[/tex]. The correct choice from the provided options is [tex]\(\frac{9}{10}\)[/tex].
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