Final answer:
The product of 2 and 3/4 multiplied by 5 and 1/3 is 14 and 2/3 after converting both mixed numbers to improper fractions, multiplying, and then simplifying.
Step-by-step explanation:
The student is asking to multiply two mixed numbers which are 2 and 3/4 and 5 and 1/3. To multiply these two numbers, start by converting each mixed number into an improper fraction. Then multiply the numerators together and the denominators together, and simplify the resulting fraction if possible. Lastly, if the fraction can be converted back into a mixed number, do so to provide the final answer.
First, convert 2 and 3/4 to an improper fraction: 2 × 4 + 3 = 11/4. Convert 5 and 1/3 to an improper fraction: 5 × 3 + 1 = 16/3. Now multiply (11/4) × (16/3), giving (11 × 16) / (4 × 3) = 176/12. Simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 4, yielding 44/3. Finally convert this improper fraction back to a mixed number: 44 ÷ 3 = 14 with a remainder of 2, so the mixed number is 14 and 2/3.