Question

Vocabulary: How are integers and their opposites related?

a) 5 + (-5) = 0
b) 0.4 + 4 = 8
c) -5 + (-5) = -10
d) All of the above

Answer 1

Integers and their opposites, when added, result in zero due to the additive inverse property. The correct answer to the provided question is 5 + (-5) = 0, as this shows a number added to its opposite equals zero.

Step-by-step explanation:

Integers and their opposites are related in that they sum up to zero, which is known as the additive inverse property. For example, when you have a positive integer and you add its opposite, which is the same number but with a negative sign, the result is zero. An instance of this is 5 + (-5) = 0. This relationship is a fundamental part of integer operations.

• When two positive numbers add, the result is positive (e.g., 3+2 = 5).
• When two negative numbers add, the result is negative (e.g., -4 + (-2) = -6).
• If you are subtracting, change the sign of the subtracted number and then add (e.g., 5 - (+3) = 5 - 3 = 2).

Moreover, multiplication rules indicate that the product of two positive numbers is positive, the product of two negative numbers is also positive, and the product of a positive number and a negative number is negative (e.g., (-3) x 2 = -6). The same rules apply to division.