Evaluate: f. `2 (1)/(3) xx 1 (5)/(28)`

Answer

To evaluate the expression \(2 \frac{1}{3} \times 1 \frac{5}{28}\), we can follow these steps:

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

1. **Convert \(2 \frac{1}{3}\)**:
- Multiply the whole number (2) by the denominator (3): \(2 \times 3 = 6\).
- Add the numerator (1) to this result: \(6 + 1 = 7\).
- So, \(2 \frac{1}{3} = \frac{7}{3}\).

2. **Convert \(1 \frac{5}{28}\)**:
- Multiply the whole number (1) by the denominator (28): \(1 \times 28 = 28\).
- Add the numerator (5) to this result: \(28 + 5 = 33\).
- So, \(1 \frac{5}{28} = \frac{33}{28}\).

### Step 2: Multiply the Improper Fractions
Now we can multiply the two improper fractions:

\[ \frac{7}{3} \times \frac{33}{28} \]

### Step 3: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:

\[ \text{Numerator: } 7 \times 33 = 231 \]
\[ \text{Denominator: } 3 \times 28 = 84 \]

So, we have:

\[ \frac{231}{84} \]

### Step 4: Simplify the Fraction
Now, we need to simplify \(\frac{231}{84}\).

1. Find the greatest common divisor (GCD) of 231 and 84.
- The prime factorization of 231 is \(3 \times 7 \times 11\).
- The prime factorization of 84 is \(2 \times 2 \times 3 \times 7\).
- The common factors are \(3\) and \(7\).

2. Divide both the numerator and denominator by their GCD (21):

\[ \frac{231 \div 21}{84 \div 21} = \frac{11}{4} \]

### Final Answer
Thus, the final answer is:

\[ \frac{11}{4} \]

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