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What is the value of the expression (2 1/2) + 4 2/3 -(+3 1/4) + 7 5/6 -(-3 1/4)?

a) 13 1/2
b) 14 3/4
c) 12 7/8
d) 15 1/4

User Maxbublis
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1 Answer

1 vote

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.

User Jedu
by
7.1k points

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