`5(1/6) // 9/2` is equal to:

Options

A. `31/6`
B. `1/27`
C. `5(1/27)`
D. `31/27`

Answer

To solve the expression \( 5\left(\frac{1}{6}\right) \div \left(\frac{9}{2}\right) \), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 5\left(\frac{1}{6}\right) \) can be converted to an improper fraction.

\[ 5\left(\frac{1}{6}\right) = \frac{5 \times 6 + 1}{6} = \frac{30 + 1}{6} = \frac{31}{6} \]

### Step 2: Write the division as multiplication
Now, we need to divide by \( \frac{9}{2} \). Dividing by a fraction is the same as multiplying by its reciprocal.

\[ \frac{31}{6} \div \frac{9}{2} = \frac{31}{6} \times \frac{2}{9} \]

### Step 3: Multiply the fractions
Now we multiply the numerators and the denominators:

\[ \frac{31 \times 2}{6 \times 9} = \frac{62}{54} \]

### Step 4: Simplify the fraction
To simplify \( \frac{62}{54} \), we can find the greatest common divisor (GCD) of 62 and 54, which is 2.

\[ \frac{62 \div 2}{54 \div 2} = \frac{31}{27} \]

### Final Answer
Thus, the expression \( 5\left(\frac{1}{6}\right) \div \left(\frac{9}{2}\right) \) is equal to \( \frac{31}{27} \).

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