To find the quotient of [tex]\( \frac{5}{31} \div \frac{15}{23} \)[/tex], follow these steps:
1. Identify the Division of Fractions:
[tex]\[
\frac{\frac{5}{31}}{\frac{15}{23}}
\][/tex]
2. Convert the Division to Multiplication by Reciprocal:
When dividing fractions, you multiply by the reciprocal of the divisor. So,
[tex]\[
\frac{5}{31} \div \frac{15}{23} = \frac{5}{31} \times \frac{23}{15}
\][/tex]
3. Multiply the Fractions:
Multiply the numerators and the denominators:
[tex]\[
\frac{5 \times 23}{31 \times 15} = \frac{115}{465}
\][/tex]
4. Simplify the Fraction:
To simplify [tex]\( \frac{115}{465} \)[/tex], find the greatest common divisor (GCD) of 115 and 465. The GCD is 5.
[tex]\[
\frac{115 \div 5}{465 \div 5} = \frac{23}{93}
\][/tex]
So, the quotient of [tex]\( \frac{5}{31} \div \frac{15}{23} \)[/tex] simplified to the lowest terms is:
[tex]\[
\frac{23}{93}
\][/tex]
Therefore, the correct answer is:
B. [tex]\( \frac{23}{93} \)[/tex]
