Question

Consider the problem.

−1 3/4÷2/5

Determine the quotient in simplest form.

(1 point)
Responses

438
4 and 3 eighths

−438
negative 4 and 3 eighths

−1420
negative 14 over 20

358
35 eighths
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Answer 1

To solve the problem \(-1 \frac{3}{4} \div \frac{2}{5}\), we first need to convert the mixed number \(-1 \frac{3}{4}\) into an improper fraction.

1. Convert \(-1 \frac{3}{4}\) to an improper fraction:
\[
-1 \frac{3}{4} = -\left(1 \cdot 4 + 3\right) / 4 = -\left(4 + 3\right) / 4 = -\frac{7}{4}
\]

2. Now, we divide \(-\frac{7}{4}\) by \(\frac{2}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal:
\[
-\frac{7}{4} \div \frac{2}{5} = -\frac{7}{4} \cdot \frac{5}{2}
\]

3. Multiply the fractions:
\[
-\frac{7 \cdot 5}{4 \cdot 2} = -\frac{35}{8}
\]

4. The result \(-\frac{35}{8}\) can be expressed as a mixed number:
\[
-\frac{35}{8} = -4 \frac{3}{8}
\]

Thus, the quotient in simplest form is \( \text{negative } 4 \text{ and } 3 \text{ eighths} \).

**The correct response is:**
**−4 and 3 eighths**