Find the quotient of 5/31 divided by 15/23. Reduce your answer to the lowest fraction.

Question

Question 7 options:

A)

93/23, or 41/23

B)

115/465

C)

75/373

D)

23/93

Answer 1

To divide fractions, you multiply by the reciprocal of the divisor. So, to find \( \frac{5}{31} \div \frac{15}{23} \), you multiply \( \frac{5}{31} \) by the reciprocal of \( \frac{15}{23} \):

\[ \frac{5}{31} \div \frac{15}{23} = \frac{5}{31} \times \frac{23}{15} \]

Now, multiply the fractions:

\[ \frac{5 \times 23}{31 \times 15} = \frac{115}{465} \]

Next, we reduce the fraction \( \frac{115}{465} \). To do this, we find the greatest common divisor (GCD) of 115 and 465.

The prime factorization of 115 is \( 5 \times 23 \), and for 465, we factor it as follows:

1. Divide by 5: \( 465 \div 5 = 93 \)
2. Factor 93: \( 93 = 3 \times 31 \)

Thus, \( 465 = 5 \times 3 \times 31 \).

Now, we see the common factor:

• The GCD of \( 115 \) and \( 465 \) is \( 5 \).

Now, divide both the numerator and the denominator by \( 5 \):

\[ \frac{115 \div 5}{465 \div 5} = \frac{23}{93} \]

Therefore, the reduced form of \( \frac{115}{465} \) is \( \frac{23}{93} \).

Thus, the answer is:

D) \( \frac{23}{93} \)