18 boxes of nails weigh equally and their total weight is `49 1/2` kg. How much does each box weigh?

Answer

To find the weight of each box of nails, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
The total weight of the boxes is given as \( 49 \frac{1}{2} \) kg. We can convert this mixed number into an improper fraction.

\[ 49 \frac{1}{2} = \frac{49 \times 2 + 1}{2} = \frac{98 + 1}{2} = \frac{99}{2} \text{ kg} \]

### Step 2: Divide the total weight by the number of boxes.
Now that we have the total weight in improper fraction form, we need to divide this by the number of boxes, which is 18.

\[ \text{Weight of each box} = \frac{99/2}{18} \]

### Step 3: Simplify the division.
To simplify the division of a fraction by a whole number, we can multiply the denominator of the fraction by the whole number.

\[ \frac{99/2}{18} = \frac{99}{2 \times 18} = \frac{99}{36} \]

### Step 4: Simplify the fraction.
Now, we can simplify \( \frac{99}{36} \) by finding the greatest common divisor (GCD) of 99 and 36. The GCD is 9.

\[ \frac{99 \div 9}{36 \div 9} = \frac{11}{4} \]

### Step 5: Convert the improper fraction to a mixed number.
To express \( \frac{11}{4} \) as a mixed number, we divide 11 by 4.

\[ 11 \div 4 = 2 \quad \text{(remainder 3)} \]

So, \( \frac{11}{4} = 2 \frac{3}{4} \) kg.

### Final Answer:
The weight of each box is \( 2 \frac{3}{4} \) kg.

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