Question

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

Answer 1

To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), first convert \(-2 \frac{3}{5}\) to an improper fraction.

1. Convert \(-2 \frac{3}{5}\) to an improper fraction:
\[
-2 \frac{3}{5} = -\left(2 \times 5 + 3\right)/5 = -\left(10 + 3\right)/5 = -\frac{13}{5}
\]

2. Now divide \(-\frac{13}{5}\) by \(\frac{4}{5}\):
\[
-\frac{13}{5} \div \frac{4}{5}
\]
To divide by a fraction, multiply by its reciprocal:
\[
-\frac{13}{5} \times \frac{5}{4}
\]

3. Multiply the fractions:
\[
= -\frac{13 \times 5}{5 \times 4} = -\frac{65}{20}
\]

4. Simplify \(-\frac{65}{20}\):
The numerator and denominator can both be divided by 5:
\[
-\frac{65 \div 5}{20 \div 5} = -\frac{13}{4}
\]

So, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is \(-\frac{13}{4}\).