`(4)2/17div(1)2/5xx(2)2/33=?`

Options

A. 4 `2/33`
B. 6 `2/33`
C. 6 `1/11`
D. 8 `1/11`

Answer

To solve the expression \( (4) \frac{2}{17} \div (1) \frac{2}{5} \times (2) \frac{2}{33} \), we will follow these steps:

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

1. \( 4 \frac{2}{17} = \frac{4 \times 17 + 2}{17} = \frac{68 + 2}{17} = \frac{70}{17} \)
2. \( 1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5} \)
3. \( 2 \frac{2}{33} = \frac{2 \times 33 + 2}{33} = \frac{66 + 2}{33} = \frac{68}{33} \)

So, we rewrite the expression as:
\[ \frac{70}{17} \div \frac{7}{5} \times \frac{68}{33} \]

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

\[ \frac{70}{17} \times \frac{5}{7} \times \frac{68}{33} \]

### Step 3: Multiply the Fractions
Now, we multiply the fractions together. We can multiply the numerators and the denominators separately.

\[ \text{Numerator: } 70 \times 5 \times 68 \]
\[ \text{Denominator: } 17 \times 7 \times 33 \]

Calculating the numerator:
\[ 70 \times 5 = 350 \]
\[ 350 \times 68 = 23800 \]

Calculating the denominator:
\[ 17 \times 7 = 119 \]
\[ 119 \times 33 = 3927 \]

So, we have:
\[ \frac{23800}{3927} \]

### Step 4: Simplify the Fraction
Now we check if we can simplify \( \frac{23800}{3927} \).

Since 23800 and 3927 have no common factors, we can conclude that this is the simplest form.

### Final Answer
Thus, the value of the expression \( (4) \frac{2}{17} \div (1) \frac{2}{5} \times (2) \frac{2}{33} \) is:
\[ \frac{23800}{3927} \]