Simplify
`78(3)/(4)divide2(1)/(2)=?`

Options

A. `31(1)/(2)`
B. `39(3)/(8)`
C. `40(1)/(3)`
D. none of these

Answer

To simplify the expression \( 78 \frac{3}{4} \div 2 \frac{1}{2} \), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 78 \frac{3}{4} \):
\[ 78 \frac{3}{4} = \frac{(78 \times 4) + 3}{4} = \frac{312 + 3}{4} = \frac{315}{4} \]

For \( 2 \frac{1}{2} \):
\[ 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]

### Step 2: Rewrite the Division as Multiplication
Now we rewrite the division of fractions as multiplication by the reciprocal of the second fraction:
\[ \frac{315}{4} \div \frac{5}{2} = \frac{315}{4} \times \frac{2}{5} \]

### Step 3: Multiply the Fractions
Now we multiply the fractions:
\[ \frac{315 \times 2}{4 \times 5} = \frac{630}{20} \]

### Step 4: Simplify the Resulting Fraction
Next, we simplify \( \frac{630}{20} \):
\[ \frac{630 \div 10}{20 \div 10} = \frac{63}{2} \]

### Step 5: Convert to Mixed Number (if needed)
If we want to convert \( \frac{63}{2} \) back to a mixed number:
\[ 63 \div 2 = 31 \quad \text{remainder } 1 \quad \Rightarrow \quad 31 \frac{1}{2} \]

### Final Answer
Thus, the simplified result of \( 78 \frac{3}{4} \div 2 \frac{1}{2} \) is:
\[ 31 \frac{1}{2} \quad \text{or} \quad \frac{63}{2} \]

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