How many `1/6` are there in `3(1)/3` ?

Options

A. 4
B. 5
C. 8
D. 20

Answer

To solve the question "How many \( \frac{1}{6} \) are there in \( 3 \frac{1}{3} \)?", we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
First, we need to convert \( 3 \frac{1}{3} \) into an improper fraction.

\[ 3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]

### Step 2: Set up the equation
Next, we want to find out how many \( \frac{1}{6} \) are in \( \frac{10}{3} \). We can let \( x \) be the number of \( \frac{1}{6} \) in \( \frac{10}{3} \).

\[ x \cdot \frac{1}{6} = \frac{10}{3} \]

### Step 3: Solve for \( x \)
To find \( x \), we can rearrange the equation:

\[ x = \frac{10}{3} \div \frac{1}{6} \]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ x = \frac{10}{3} \times 6 \]

### Step 4: Perform the multiplication
Now, we can multiply:

\[ x = \frac{10 \times 6}{3} = \frac{60}{3} = 20 \]

### Conclusion
Thus, there are 20 \( \frac{1}{6} \) in \( 3 \frac{1}{3} \).

### Final Answer
The answer is \( 20 \).

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