`17(2)/(5)xx4(5)/(8)-?=46(7)/(8)`

Options

A. `32(3)/(5)`
B. `33(3)/(5)`
C. `33(2)/(5)`
D. `32(2)/(5)`

Explanation

To solve the equation \( \frac{72}{5} \times \frac{45}{8} - ? = \frac{46}{8} \), we will follow these steps:

### Step 1: Calculate \( \frac{72}{5} \times \frac{45}{8} \)

To multiply the fractions, we multiply the numerators together and the denominators together:

\[ \frac{72 \times 45}{5 \times 8} \]

Calculating the numerator:

\[ 72 \times 45 = 3240 \]

Calculating the denominator:

\[ 5 \times 8 = 40 \]

So we have:

\[ \frac{72}{5} \times \frac{45}{8} = \frac{3240}{40} \]

### Step 2: Simplify \( \frac{3240}{40} \)

Now we simplify \( \frac{3240}{40} \):

\[ \frac{3240 \div 40}{40 \div 40} = \frac{81}{1} = 81 \]

### Step 3: Rewrite the equation

Now we rewrite the equation with the calculated value:

\[ 81 - ? = \frac{46}{8} \]

### Step 4: Convert \( \frac{46}{8} \) to a simpler form

We can simplify \( \frac{46}{8} \):

\[ \frac{46 \div 2}{8 \div 2} = \frac{23}{4} \]

### Step 5: Solve for \( ? \)

Now we have:

\[ 81 - ? = \frac{23}{4} \]

To isolate \( ? \), we rearrange the equation:

\[ ? = 81 - \frac{23}{4} \]

### Step 6: Convert 81 to a fraction with a denominator of 4

To subtract \( \frac{23}{4} \) from 81, we convert 81 into a fraction:

\[ 81 = \frac{81 \times 4}{4} = \frac{324}{4} \]

### Step 7: Perform the subtraction

Now we perform the subtraction:

\[ ? = \frac{324}{4} - \frac{23}{4} = \frac{324 - 23}{4} = \frac{301}{4} \]

### Step 8: Final answer

Thus, the value of \( ? \) is:

\[ ? = \frac{301}{4} = 75.25 \]