Final answer:
Multiplication of positive and negative fractions involves following sign rules and directly multiplying numerators and denominators, while adding and subtracting requires finding a common denominator before combining the numerators, and then applying sign rules.
Step-by-step explanation:
Multiplying positive and negative fractions differs from adding and subtracting them due to rules concerning the signs and the operations performed. When multiplying, the product of two positive numbers or two negative numbers is positive (e.g., 2×3 = 6 or (-4) × (-3) = 12), while the product of a positive and a negative number is negative (e.g., (-3) × 2 = -6). Conversely, in addition, the sum of two positive numbers is positive, the sum of two negative numbers carries a negative sign, and for numbers with opposite signs, you subtract the smaller number from the larger one and retain the sign of the larger number (e.g., -5 + 3 = -2). When subtracting, you change the sign of the subtracted number and then proceed to add.
With fractions, for addition and subtraction, you must ensure that the fractions have a common denominator before combining them, which is a step not necessary in multiplication or division. For example, you cannot add ½ and ¼ without first converting them to have the same denominator. Once the denominators are common, you add or subtract the numerators while keeping the denominator the same. With multiplication of fractions, you simply multiply the numerators together and the denominators together, and simplify afterwards if possible. This is different from the procedure for addition and subtraction, which involves finding a common denominator before combining the numerators.