A pile of notebooks is 14 `1/4` cm thick. If each notebook is 1 `3/16` cm thick, then find the 4 16 number of notebooks in the pile

Answer

To find the number of notebooks in the pile, we need to divide the total thickness of the pile by the thickness of each notebook. Let's break down the solution step by step.

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

1. **Total thickness of the pile:**
- \( 14 \frac{1}{4} \) cm can be converted as follows:
\[ 14 \frac{1}{4} = 14 + \frac{1}{4} = \frac{14 \times 4 + 1}{4} = \frac{56 + 1}{4} = \frac{57}{4} \text{ cm} \]

2. **Thickness of each notebook:**
- \( 1 \frac{3}{16} \) cm can be converted as follows:
\[ 1 \frac{3}{16} = 1 + \frac{3}{16} = \frac{1 \times 16 + 3}{16} = \frac{16 + 3}{16} = \frac{19}{16} \text{ cm} \]

### Step 2: Set Up the Division
Now we can set up the division to find the number of notebooks:
\[ \text{Number of notebooks} = \frac{\text{Total thickness}}{\text{Thickness of each notebook}} = \frac{\frac{57}{4}}{\frac{19}{16}} \]

### Step 3: Apply the Division of Fractions Rule
To divide fractions, we multiply by the reciprocal of the divisor:
\[ \frac{57}{4} \div \frac{19}{16} = \frac{57}{4} \times \frac{16}{19} \]

### Step 4: Multiply the Fractions
Now we multiply the fractions:
\[ \frac{57 \times 16}{4 \times 19} \]

### Step 5: Simplify the Expression
Now we can simplify:
1. Calculate \( 57 \times 16 = 912 \)
2. Calculate \( 4 \times 19 = 76 \)

So we have:
\[ \frac{912}{76} \]

### Step 6: Simplify Further
Now we simplify \( \frac{912}{76} \):
- Divide both the numerator and denominator by 4:
\[ \frac{912 \div 4}{76 \div 4} = \frac{228}{19} \]

### Step 7: Perform the Division
Now we perform the division:
\[ 228 \div 19 = 12 \]

### Conclusion
Thus, the total number of notebooks in the pile is **12**.

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