30. $$ w \div 3 \frac{3}{5}=-8 \frac{2}{5} $$

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UpStudy AI · Accepted Answer

We start with the equation
$$
w \div 3\frac{3}{5} = -8\frac{2}{5}.
$$

**Step 1. Convert the Mixed Numbers to Improper Fractions**

Convert $$3\frac{3}{5}$$ to an improper fraction:
$$
3\frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5}.
$$

Convert $$-8\frac{2}{5}$$ to an improper fraction:
$$
-8\frac{2}{5} = \frac{-8 \times 5 - 2}{5} = \frac{-40 - 2}{5} = \frac{-42}{5}.
$$

**Step 2. Rewrite the Equation**

The equation becomes:
$$
\frac{w}{\frac{18}{5}} = \frac{-42}{5}.
$$

**Step 3. Solve for $$w$$**

To isolate $$w$$, multiply both sides of the equation by $$\frac{18}{5}$$:
$$
w = \frac{-42}{5} \times \frac{18}{5}.
$$

Multiply the numerators and the denominators:
$$
w = \frac{-42 \times 18}{5 \times 5} = \frac{-756}{25}.
$$

**Step 4. Express the Answer**

The solution can be expressed as an improper fraction:
$$
w = \frac{-756}{25}.
$$

Alternatively, convert $$\frac{-756}{25}$$ to a mixed number by dividing 756 by 25:
$$
756 \div 25 = 30 \text{ with a remainder of } 6,
$$
so
$$
w = -30\frac{6}{25}.
$$
$$ w = -30\frac{6}{25} $$

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