Two packets of sweets weight `2 (7)/(8) kg and 3 (1)/(4) kg ` respectively. How much is the total weight of the sweets ?

Options

A. `5 (1)/(8) kg `
B. `6 (1)/(8) kg `
C. `(39)/(8) kg `
D. `(57)/(8) kg `

Answer

To find the total weight of the two packets of sweets, we need to add their weights together. The weights given are \(2 \frac{7}{8} \, \text{kg}\) and \(3 \frac{1}{4} \, \text{kg}\).

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

For \(2 \frac{7}{8}\):
\[ 2 \frac{7}{8} = \frac{(2 \times 8) + 7}{8} = \frac{16 + 7}{8} = \frac{23}{8} \]

For \(3 \frac{1}{4}\):
\[ 3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]

### Step 2: Find a Common Denominator
Next, we need to find a common denominator to add the two fractions. The denominators are 8 and 4. The least common multiple (LCM) of 8 and 4 is 8.

### Step 3: Convert the Second Fraction
Since the first fraction is already with a denominator of 8, we need to convert the second fraction \(\frac{13}{4}\) to have a denominator of 8:
\[ \frac{13}{4} = \frac{13 \times 2}{4 \times 2} = \frac{26}{8} \]

### Step 4: Add the Two Fractions
Now we can add the two fractions:
\[ \frac{23}{8} + \frac{26}{8} = \frac{23 + 26}{8} = \frac{49}{8} \]

### Step 5: Convert the Improper Fraction to a Mixed Number
Finally, we convert \(\frac{49}{8}\) back to a mixed number:
\[ 49 \div 8 = 6 \quad \text{(remainder 1)} \]
So, \(\frac{49}{8} = 6 \frac{1}{8}\).

### Final Answer
The total weight of the sweets is \(6 \frac{1}{8} \, \text{kg}\).

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