-7 1/5 divided by 4/5 in simplest form

1 answer

To divide \(-7 \frac{1}{5}\) by \(\frac{4}{5}\), we first convert the mixed number into an improper fraction.

  1. Convert \(-7 \frac{1}{5}\): \[ -7 \frac{1}{5} = -\left(7 \times 5 + 1\right)/5 = -\left(35 + 1\right)/5 = -\frac{36}{5} \]

  2. Now, we divide by \(\frac{4}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{36}{5} \div \frac{4}{5} = -\frac{36}{5} \times \frac{5}{4} \]

  3. Multiply the fractions: \[ -\frac{36 \cdot 5}{5 \cdot 4} = -\frac{36}{4} \]

  4. Simplify \(-\frac{36}{4}\): \[ -\frac{36}{4} = -9 \]

Thus, \(-7 \frac{1}{5}\) divided by \(\frac{4}{5}\) is \(-9\).