What is the additive inverse of -7? A. -7 B.
C.
D. 7
The Correct Answer and Explanation is:
Correct Answer: D. 7
Explanation:
The additive inverse of a number is a value that, when added to the original number, gives a sum of zero. In other words, the additive inverse of a number “x” is the number “–x” such that:x+(–x)=0x + (–x) = 0x+(–x)=0
In this case, the number given is –7. To find its additive inverse, we ask:–7+?=0–7 + ? = 0–7+?=0
The number that satisfies this equation is +7 because:–7+7=0–7 + 7 = 0–7+7=0
Therefore, the additive inverse of –7 is 7.
Why this concept is important:
Understanding additive inverses is a foundational concept in algebra and arithmetic. It is closely tied to the properties of integers and helps in solving equations, simplifying expressions, and understanding symmetry on the number line.
The number line is an effective visual tool for understanding this idea. If you move seven units to the left of zero (–7), then move seven units to the right (+7), you return to zero. The numbers –7 and 7 are located at equal distances from zero but in opposite directions. This is what makes them additive inverses of each other.
Real-world example:
Imagine a situation in which your bank account is overdrawn by $7, meaning you have –$7. If someone deposits $7 into your account, your balance becomes zero. The $7 deposit cancels out the –$7 debt. That deposit represents the additive inverse of –7.
In mathematics, every number has an additive inverse. Zero is the only number that is its own additive inverse because:0+0=00 + 0 = 00+0=0
This concept is part of the properties of real numbers and is used extensively in algebraic problem solving.
