Final answer:
The student's task is to identify the expressions that are equivalent to 3/4. After simplifying each option, expressions C (5/6 - 1/12) and E (1 7/20 - 3/5) are found to be correct as they both simplify to 3/4.
Step-by-step explanation:
The student is asked to choose all of the expressions that are equal to 3/4. To find these expressions, we must perform the arithmetic to check each one.
- A. 8/15 - 5/11: Different denominators. This requires finding a common denominator, but it can be seen that the result will not be 3/4.
- B. 7/12 + 1/6: Convert to common denominator: (7*2 + 1) / 24 is 15/24, which simplifies to 5/8. Not equal to 3/4.
- C. 5/6 - 1/12: Convert to common denominator: (5*2 - 1) / 12 is 9/12, which simplifies to 3/4. Correct.
- D. 1 + 1/4: Converting to an improper fraction: (1*4 + 1) / 4 equals 5/4. Not equal to 3/4.
- E. 1 7/20 - 3/5: Convert mixed number to improper fraction: (1*20 + 7) / 20, and 3/5 to 12/20, then subtract: 27/20 - 12/20 equals 15/20, which simplifies to 3/4. Correct.