Explanation:
First, we need to perform the multiplication operation within the parentheses, following the order of operations:
2⅓ × 1¼ = (7/3) × (5/4) = 35/12
Now, we can substitute the values in the expression:
3½ - (2⅓ × 1¼) + ⅗ = 7/2 - 35/12 + 3/5
To add or subtract fractions with different denominators, we need to find a common denominator. The least common multiple of 2, 12, and 5 is 60, so we can rewrite the fractions with this denominator:
7/2 - 35/12 + 3/5 = (210/60) / (2/2) - (175/60) / (12/12) + (36/60) / (5/5)
Simplifying the fractions within the parentheses:
= 210/60 - 175/60 + 36/60
= 71/60
Therefore, 3½ - (2⅓ × 1¼) + ⅗ simplifies to 71/60.