Question

3 and 4/5 divided by (negative one and one/5)

Answer 1

To divide \( 3 \frac{4}{5} \) by \( -1 \frac{1}{5} \), we first convert both mixed numbers to improper fractions.

1. Convert \( 3 \frac{4}{5} \):
\[
3 \frac{4}{5} = 3 \cdot 5 + 4 = 15 + 4 = 19
\]
So, \( 3 \frac{4}{5} = \frac{19}{5} \).

2. Convert \( -1 \frac{1}{5} \):
\[
-1 \frac{1}{5} = -1 \cdot 5 - 1 = -5 - 1 = -6
\]
So, \( -1 \frac{1}{5} = -\frac{6}{5} \).

Now we can rewrite the division as:
\[
\frac{19}{5} \div -\frac{6}{5}
\]

To divide by a fraction, we multiply by its reciprocal:
\[
\frac{19}{5} \times -\frac{5}{6}
\]

Now, multiply the fractions:
\[
= \frac{19 \cdot (-5)}{5 \cdot 6} = \frac{-95}{30}
\]

Now we simplify \(\frac{-95}{30}\). Both 95 and 30 can be divided by 5:
\[
= \frac{-95 \div 5}{30 \div 5} = \frac{-19}{6}
\]

Thus, the result of \( 3 \frac{4}{5} \div (-1 \frac{1}{5}) \) is:
\[
\boxed{-\frac{19}{6}}
\]