A carton contains 16 boxes of nails and each box weighs `4 3/4` kg. How much would a carton of nails weigh?

Answer

To find the total weight of a carton containing 16 boxes of nails, where each box weighs \(4 \frac{3}{4}\) kg, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The weight of one box is given as \(4 \frac{3}{4}\) kg. To convert this to an improper fraction:

1. Multiply the whole number (4) by the denominator (4):
\[ 4 \times 4 = 16 \]
2. Add the numerator (3) to this product:
\[ 16 + 3 = 19 \]
3. Place this result over the original denominator (4):
\[ 4 \frac{3}{4} = \frac{19}{4} \text{ kg} \]

### Step 2: Multiply the weight of one box by the number of boxes
Now that we have the weight of one box as \(\frac{19}{4}\) kg, we need to find the total weight of 16 boxes:

\[ \text{Total weight} = \text{Weight of one box} \times \text{Number of boxes} \]
\[ \text{Total weight} = \frac{19}{4} \times 16 \]

### Step 3: Simplify the multiplication
To multiply \(\frac{19}{4}\) by 16, we can rewrite 16 as a fraction:

\[ 16 = \frac{16}{1} \]

Now, multiply the fractions:

\[ \frac{19}{4} \times \frac{16}{1} = \frac{19 \times 16}{4 \times 1} = \frac{304}{4} \]

### Step 4: Simplify the fraction
Now, we simplify \(\frac{304}{4}\):

\[ \frac{304}{4} = 76 \]

### Conclusion
Therefore, the total weight of the carton of nails is **76 kg**.

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