Question
Calculate the product of 8/15, 6/5, and 1/3.
Question 16 options:
A)
16/75
B)
48/15
C)
16/15
D)
48/30
Question 16 options:
A)
16/75
B)
48/15
C)
16/15
D)
48/30
Answers
GPT-4o mini
To find the product of the fractions \( \frac{8}{15} \), \( \frac{6}{5} \), and \( \frac{1}{3} \), we multiply the numerators together and the denominators together.
1. Multiply the numerators:
\[
8 \times 6 \times 1 = 48
\]
2. Multiply the denominators:
\[
15 \times 5 \times 3 = 225
\]
3. Now we can express the product as:
\[
\frac{48}{225}
\]
Next, we can simplify \( \frac{48}{225} \) by finding the greatest common divisor (GCD) of 48 and 225.
- The prime factorization of 48 is \( 2^4 \times 3 \).
- The prime factorization of 225 is \( 3^2 \times 5^2 \).
The common factor is \( 3 \).
4. We can divide both the numerator and the denominator by \( 3 \):
\[
\frac{48 \div 3}{225 \div 3} = \frac{16}{75}
\]
Thus, the simplified product of the fractions is \( \frac{16}{75} \).
Therefore, the correct answer is:
**A) \(\frac{16}{75}\)**.
1. Multiply the numerators:
\[
8 \times 6 \times 1 = 48
\]
2. Multiply the denominators:
\[
15 \times 5 \times 3 = 225
\]
3. Now we can express the product as:
\[
\frac{48}{225}
\]
Next, we can simplify \( \frac{48}{225} \) by finding the greatest common divisor (GCD) of 48 and 225.
- The prime factorization of 48 is \( 2^4 \times 3 \).
- The prime factorization of 225 is \( 3^2 \times 5^2 \).
The common factor is \( 3 \).
4. We can divide both the numerator and the denominator by \( 3 \):
\[
\frac{48 \div 3}{225 \div 3} = \frac{16}{75}
\]
Thus, the simplified product of the fractions is \( \frac{16}{75} \).
Therefore, the correct answer is:
**A) \(\frac{16}{75}\)**.