Final answer:
To simplify the expression 2/3−3/2×(3²−17/3), follow the order of operations and simplify the expression step by step. The final simplified expression is 13/3.
Step-by-step explanation:
To simplify the expression 2/3−3/2×(3²−17/3), we need to follow the order of operations, which is parentheses first, then multiplication/division, and finally addition/subtraction.
Step 1: Simplify the expression inside the parentheses:
3²−17/3 = 9−17/3 = 9−(17/3)
Step 2: Multiply the resulting value by 3/2:
(9−(17/3))×(3/2) = (27/3−(17/3))×(3/2) = 10/3×(3/2)
Step 3: Subtract 2/3 from the previous result:
(10/3×(3/2))−(2/3) = (10/2)−(2/3) = 5−(2/3)
Step 4: Convert the subtraction into a common denominator:
5−(2/3) = (15/3)−(2/3)
Step 5: Perform the subtraction:
(15/3)−(2/3) = 13/3
Therefore, the simplified expression is 13/3.