Final answer:
Integers have signs (+ve or -ve) that indicate their relation to zero, with their operations following specific rules. The sum or product of numbers with the same sign is positive, while the combination of numbers with opposite signs depends on their relative sizes and operations.
Step-by-step explanation:
Understanding whether an integer is positive (+ve) or negative (-ve) is crucial in correctly interpreting mathematical operations and real-world situations. When numbers have the same sign and are added together, the resulting integer will take that same sign; for example, adding two positive numbers like 3 + 2 will result in a positive sum of 5. In contrast, combining two negative numbers, such as -4 + (-2), will result in a negative sum of -6.
However, when adding numbers with opposite signs, we must subtract the smaller absolute value from the larger one, and the result takes the sign of the larger number. So, -5 + 3 equals -2. Subtraction involves changing the sign of the number being subtracted and then following addition rules. For instance, to subtract 3 from 5, you change the sign of 3 to become -3 and then add it to 5, resulting in 5 - 3 = 2.
Multiplication and division follow a similar pattern regarding the sign of the result. Multiplying two positive numbers or two negative numbers results in a positive product, such as 2 x 3 yielding 6, and (-4) x (-3) yielding 12. When the numbers being multiplied have opposite signs, the product is negative, as seen in (-3) x 2 equaling -6 and 4 x (-4) equaling -16.