`32000xx(3)/(4)xx?xx(1)/(2)=4800`

Options

A. `2/3`
B. `3/5`
C. `2/5`
D. `1/4`

Explanation

To solve the equation \( 32000 \times \frac{3}{4} \times ? \times \frac{1}{2} = 4800 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ 32000 \times \frac{3}{4} \times ? \times \frac{1}{2} = 4800 \]

### Step 2: Simplify the left side
First, we can simplify the left side by multiplying \( \frac{3}{4} \) and \( \frac{1}{2} \):
\[ \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8} \]
So the equation becomes:
\[ 32000 \times ? \times \frac{3}{8} = 4800 \]

### Step 3: Isolate the question mark
To isolate the question mark, we can multiply both sides by \( \frac{8}{3} \):
\[ 32000 \times ? = 4800 \times \frac{8}{3} \]

### Step 4: Calculate the right side
Now we calculate \( 4800 \times \frac{8}{3} \):
\[ 4800 \times \frac{8}{3} = \frac{4800 \times 8}{3} = \frac{38400}{3} = 12800 \]
So now we have:
\[ 32000 \times ? = 12800 \]

### Step 5: Solve for ?
Now we can solve for \( ? \) by dividing both sides by 32000:
\[ ? = \frac{12800}{32000} \]

### Step 6: Simplify the fraction
We can simplify \( \frac{12800}{32000} \):
\[ ? = \frac{128}{320} = \frac{128 \div 16}{320 \div 16} = \frac{8}{20} = \frac{2}{5} \]

### Final Answer
Thus, the value of \( ? \) is:
\[ ? = \frac{2}{5} \]

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