Final answer:
The important relation between addition and subtraction preserved in fractions is the commutative property which states A + B = B + A. We use intuition and the need for a common denominator to add or subtract fractions. Multiplication of fractions involves multiplying the numerators and denominators directly.
Step-by-step explanation:
An important relation between addition and subtraction that is preserved in fractions is the commutative property of addition, which states that A + B is equal to B + A. This property holds true for both whole numbers and fractions. Our intuition can assist us in figuring out addition and subtraction of fractions by knowing that like denominators are needed to add or subtract fractions directly. We need to find a common denominator, and we do this by finding the least common multiple of the two denominators. For example, adding ½ and ⅓ we find a common denominator of 6, turning the fractions into &frac36; and &frac26;. Now we can add the numerators to get ⅚.
Our natural intuition also helps us understand that multiplication is related to division, as dividing by a number is the same as multiplying by its reciprocal. When we multiply fractions, we simply multiply the numerators together and the denominators together. For instance, ½ × ⅓ will be ⅙.