Simplify 3 1/2 + 1 1/4 - 2 2/3

To simplify the given expression, we need to convert all the mixed numbers to improper fractions and then perform the addition and subtraction.

The improper fraction form of 3 1/2 is (2*3 + 1)/2 = 7/2.
The improper fraction form of 1 1/4 is (4*1 + 1)/4 = 5/4.
The improper fraction form of 2 2/3 is (3*2 + 2)/3 = 8/3.

Now we can substitute these fractions back into the original expression:

3 1/2 + 1 1/4 - 2 2/3 = 7/2 + 5/4 - 8/3

To combine the fractions, we need to find a common denominator. In this case, the common denominator is 2 * 4 * 3 = 24.

Multiplying the numerators and denominators by the appropriate factors to get the common denominator, we get:

(7/2) * (12/12) + (5/4) * (6/6) - (8/3) (8/8)
= 84/24 + 30/24 - 64/24

Now that all the fractions have a common denominator, we can combine them:

84/24 + 30/24 - 64/24 = (84 + 30 - 64)/24 = 50/24

To simplify the fraction, we can reduce it by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case:

50/24 = (25/2) / (12/2) = 25/12

Therefore, the simplified form of 3 1/2 + 1 1/4 - 2 2/3 is 25/12.