Final answer:
The value of the expression is calculated by converting mixed numbers to improper fractions, finding a common denominator, and then adding or subtracting the numerators. The result is simplified to 15, which matches none of the given options exactly because the provided options include fractions.
Step-by-step explanation:
The value of the expression (2 1/2) + 4 2/3 -(+3 1/4) + 7 5/6 -(-3 1/4) can be calculated by first simplifying each term to have common denominators and then combining like terms. Here's the step-by-step calculation:
- Convert mixed numbers to improper fractions:
- (2 1/2) becomes 5/2
- 4 2/3 becomes 14/3
- (+3 1/4) becomes 13/4
- 7 5/6 becomes 47/6
- (-3 1/4) becomes -13/4
Now, add and subtract the terms:
- (5/2) + (14/3) - (13/4) + (47/6) + (13/4)
- To combine, find a common denominator. The smallest common denominator for 2, 3, 4, and 6 is 12.
- This results in:
- (30/12) + (56/12) - (39/12) + (94/12) + (39/12)
- Combine the numerators:
- (30 + 56 - 39 + 94 + 39) / 12
- Simplify:
- 180/12
- Which is further simplified to 15
Thus, the value of the expression is 15, which corresponds to option (d) 15 1/4 if we consider standard form as 15 0/4, but there seems to be some discrepancy as we don't have fractions in the final result.