Question
Evaluate 5/2÷7/4 and simplify your answer completely.(1 point)
Responses
9/9
9 ninths
35/8
35 eighths
12/6
12 sixths
10/7
Responses
9/9
9 ninths
35/8
35 eighths
12/6
12 sixths
10/7
Answers
GPT-4o mini
To evaluate \( \frac{5}{2} \div \frac{7}{4} \), you can multiply by the reciprocal of the second fraction:
\[
\frac{5}{2} \div \frac{7}{4} = \frac{5}{2} \times \frac{4}{7}
\]
Now, multiply the numerators and the denominators:
\[
\frac{5 \times 4}{2 \times 7} = \frac{20}{14}
\]
Next, simplify \( \frac{20}{14} \) by finding the greatest common divisor (GCD) of 20 and 14. The GCD is 2. Now divide both the numerator and denominator by 2:
\[
\frac{20 \div 2}{14 \div 2} = \frac{10}{7}
\]
Thus, the simplified answer is:
\[
\frac{10}{7}
\]
So the correct response is:
**10/7**
\[
\frac{5}{2} \div \frac{7}{4} = \frac{5}{2} \times \frac{4}{7}
\]
Now, multiply the numerators and the denominators:
\[
\frac{5 \times 4}{2 \times 7} = \frac{20}{14}
\]
Next, simplify \( \frac{20}{14} \) by finding the greatest common divisor (GCD) of 20 and 14. The GCD is 2. Now divide both the numerator and denominator by 2:
\[
\frac{20 \div 2}{14 \div 2} = \frac{10}{7}
\]
Thus, the simplified answer is:
\[
\frac{10}{7}
\]
So the correct response is:
**10/7**