Final answer:
To solve ½ + (-⅙), convert both fractions to a common denominator of 6, resulting in ⅓ + (-⅙). Then add the numerators to get 2, so the expression simplifies to ⅙ or 1/3.
Step-by-step explanation:
To solve the mathematical expression ½ + (-⅙), we need to find a common denominator to combine these two fractions. To do this intuitively, we can look at the denominators, which are 2 and 6, and realize that the least common multiple of these numbers is 6. Thus, we can convert ½ to ⅓ by multiplying both the numerator and denominator by 3. Now the expression looks like this: ⅓ + (-⅙). Since the denominators are the same, we can simply add the numerators: 3 + (-1) = 2. Therefore, the sum of ½ and (-⅙) is ⅓ or 2/6, which simplifies to ⅙.
Understanding the rules of addition and multiplication for numbers with different signs is also crucial. When two positive numbers multiply, the result is positive. The same is true when two negative numbers multiply. However, when numbers with opposite signs are multiplied or divided, the result is negative. So, dividing 6 by 3 gives us 2, and dividing -1 by 6 remains -⅙. Adding these two results yields the final answer.