Questions: -6 1/3 ÷ -1 2/3 =

Transcript text: \[ -6 \frac{1}{3} \div-1 \frac{2}{3}= \]

Solution

Solution Steps

To solve the division of two mixed numbers, first convert the mixed numbers to improper fractions. Then, divide the first fraction by the second by multiplying the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction if possible.

Step 1: Convert Mixed Numbers to Improper Fractions

The mixed numbers are given as: \[ -6 \frac{1}{3} \quad \text{and} \quad -1 \frac{2}{3} \] Converting these to improper fractions: \[ -6 \frac{1}{3} = -\frac{19}{3} \quad \text{and} \quad -1 \frac{2}{3} = -\frac{5}{3} \]

Step 2: Divide the Improper Fractions

To divide the fractions, we multiply the first fraction by the reciprocal of the second: \[ -\frac{19}{3} \div -\frac{5}{3} = -\frac{19}{3} \times -\frac{3}{5} \] This simplifies to: \[ \frac{19 \cdot 3}{3 \cdot 5} = \frac{19}{5} \]

Step 3: Simplify the Result

The result \(\frac{19}{5}\) is already in its simplest form.