Question

What is the quotient when you divide-2 and 3/5 by 4/5

Answer 1

To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), we first convert the mixed number \(-2 \frac{3}{5}\) into an improper fraction.

1. Convert \(-2\) to a fraction:
\[
-2 = -\frac{10}{5}
\]
So,
\[
-2 \frac{3}{5} = -\frac{10}{5} + \frac{3}{5} = -\frac{7}{5}
\]

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

3. Multiply the fractions:
\[
-\frac{7 \times 5}{5 \times 4} = -\frac{35}{20}
\]

4. Simplify \(-\frac{35}{20}\):
- Both the numerator and denominator can be divided by 5:
\[
-\frac{35 \div 5}{20 \div 5} = -\frac{7}{4}
\]

Therefore, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is \(-\frac{7}{4}\) or \(-1 \frac{3}{4}\) in mixed number form.