A pasta recipe requires `2(2)/(3)kg` cheese. Approximately, how much pasta can be made from a 21 kg cheese ?

Options

A. `7(7)/(8)`
B. `7(4)/(8)`
C. `6(7)/(8)`
D. `6(4)/(8)`

Answer

To find out how much pasta can be made from 21 kg of cheese when the recipe requires \(2 \frac{2}{3}\) kg of cheese, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction.
The mixed fraction \(2 \frac{2}{3}\) can be converted to an improper fraction.

To do this:
1. Multiply the whole number (2) by the denominator (3):
\[ 2 \times 3 = 6 \]
2. Add the numerator (2) to this result:
\[ 6 + 2 = 8 \]
3. Place this result over the original denominator (3):
\[ 2 \frac{2}{3} = \frac{8}{3} \]

### Step 2: Determine how many times the recipe can be made with 21 kg of cheese.
Now, we need to find out how many times \( \frac{8}{3} \) kg fits into 21 kg. We do this by dividing 21 by \( \frac{8}{3} \).

To divide by a fraction, we multiply by its reciprocal:
\[ 21 \div \frac{8}{3} = 21 \times \frac{3}{8} \]

### Step 3: Perform the multiplication.
Now we can calculate:
\[ 21 \times \frac{3}{8} = \frac{21 \times 3}{8} = \frac{63}{8} \]

### Step 4: Convert the improper fraction to a mixed number.
Next, we convert \( \frac{63}{8} \) to a mixed number:
1. Divide 63 by 8:
\[ 63 \div 8 = 7 \quad \text{(whole number)} \]
Remainder:
\[ 63 - (8 \times 7) = 63 - 56 = 7 \]
2. So, \( \frac{63}{8} \) can be expressed as:
\[ 7 \frac{7}{8} \]

### Final Answer:
Therefore, from 21 kg of cheese, approximately \( 7 \frac{7}{8} \) pasta recipes can be made.

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