\begin{tabular}{l} Divide. Write your answer as a fraction or a mixed number in simplest form. \ $$ \qquad 3 \frac{1}{2} \div 2 \frac{3}{8} $$ \ \hline\end{tabular}

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UpStudy AI · Accepted Answer

To divide the mixed numbers $$ 3 \frac{1}{2} $$ and $$ 2 \frac{3}{8} $$, we will follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Divide the first fraction by the second fraction by multiplying by the reciprocal of the second fraction.
3. Simplify the resulting fraction if necessary.

### Step 1: Convert to Improper Fractions

- For $$ 3 \frac{1}{2} $$:
  $$
  3 \frac{1}{2} = 3 \times 2 + 1 = 6 + 1 = 7 \quad \text{(so, } \frac{7}{2}\text{)}
  $$

- For $$ 2 \frac{3}{8} $$:
  $$
  2 \frac{3}{8} = 2 \times 8 + 3 = 16 + 3 = 19 \quad \text{(so, } \frac{19}{8}\text{)}
  $$

### Step 2: Divide the Fractions

Now we need to divide $$ \frac{7}{2} $$ by $$ \frac{19}{8} $$:
$$
\frac{7}{2} \div \frac{19}{8} = \frac{7}{2} \times \frac{8}{19}
$$

### Step 3: Multiply the Fractions

Now we will multiply the fractions:
$$
\frac{7 \times 8}{2 \times 19} = \frac{56}{38}
$$

### Step 4: Simplify the Fraction

Now, we will simplify $$ \frac{56}{38} $$:
- The greatest common divisor (GCD) of 56 and 38 is 2.

So, we divide both the numerator and the denominator by 2:
$$
\frac{56 \div 2}{38 \div 2} = \frac{28}{19}
$$

### Final Answer

The result of $$ 3 \frac{1}{2} \div 2 \frac{3}{8} $$ is $$ \frac{28}{19} $$, which is already in simplest form.
The answer is $$ \frac{28}{19} $$.

Divide. Write your answer as a fraction or a mixed number in simplest form.

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