Solve: `12 1/2 times 3 3/5 div 1 4/5`

Options

A. 25
B. 405
C. 81
D. 45

Answer

To solve the expression \( 12 \frac{1}{2} \times 3 \frac{3}{5} \div 1 \frac{4}{5} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number into an improper fraction.

1. \( 12 \frac{1}{2} = 12 \times 2 + 1 = 24 + 1 = 25 \) so it becomes \( \frac{25}{2} \).
2. \( 3 \frac{3}{5} = 3 \times 5 + 3 = 15 + 3 = 18 \) so it becomes \( \frac{18}{5} \).
3. \( 1 \frac{4}{5} = 1 \times 5 + 4 = 5 + 4 = 9 \) so it becomes \( \frac{9}{5} \).

Now, we can rewrite the expression as:
\[ \frac{25}{2} \times \frac{18}{5} \div \frac{9}{5} \]

### Step 2: Change Division to Multiplication
Next, we change the division of fractions into multiplication by taking the reciprocal of the divisor.

\[ \frac{25}{2} \times \frac{18}{5} \times \frac{5}{9} \]

### Step 3: Simplify the Expression
Now we can simplify the expression step by step.

1. Multiply the fractions:
\[ = \frac{25 \times 18 \times 5}{2 \times 5 \times 9} \]

2. Cancel out the common factors:
- The \( 5 \) in the numerator and denominator cancels out.
- This simplifies to:
\[ = \frac{25 \times 18}{2 \times 9} \]

3. Now, we can simplify further:
- \( 18 \div 9 = 2 \)
- So we have:
\[ = \frac{25 \times 2}{2} \]

4. The \( 2 \) in the numerator and denominator cancels out:
\[ = 25 \]

### Final Answer
Thus, the final answer is \( 25 \).

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