Nine boards are stacked on the top of each other. The thickness of each board is`3 2/3` cm.How high is the stack?

Answer

To find the total height of the stack of boards, we need to multiply the thickness of one board by the total number of boards. Here is the step-by-step solution:

### Step 1: Convert the mixed number to an improper fraction
The thickness of each board is given as \(3 \frac{2}{3}\) cm. We need to convert this mixed number into an improper fraction.

\[ 3 \frac{2}{3} = \frac{(3 \times 3) + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \text{ cm} \]

### Step 2: Multiply the thickness by the number of boards
Now that we have the thickness of one board as \(\frac{11}{3}\) cm, we can find the total height of 9 boards by multiplying the thickness of one board by 9.

\[ \text{Total height} = 9 \times \frac{11}{3} \]

### Step 3: Perform the multiplication
To multiply, we can treat 9 as a fraction:

\[ 9 = \frac{9}{1} \]

Now we can multiply the fractions:

\[ \text{Total height} = \frac{9}{1} \times \frac{11}{3} = \frac{9 \times 11}{1 \times 3} = \frac{99}{3} \]

### Step 4: Simplify the fraction
Now, we simplify \(\frac{99}{3}\):

\[ \frac{99}{3} = 33 \text{ cm} \]

### Conclusion
The total height of the stack of 9 boards is **33 cm**.

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