What is the additive inverse of 7? a) 7 b) – 7 c) 0 d) 1
The Correct Answer and Explanation is:
Correct Answer:
b) –7
Explanation:
The additive inverse of a number is the value that, when added to the original number, results in zero. In simple terms, the additive inverse of a number “undoes” the effect of that number in addition.
To find the additive inverse of 7, you need a number that when added to 7 gives 0: 7+(?)=07 + (\text{?}) = 07+(?)=0
Solving for the unknown value, subtract 7 from both sides: ?=0−7=−7\text{?} = 0 – 7 = -7?=0−7=−7
Therefore, –7 is the additive inverse of 7, because: 7+(–7)=07 + (–7) = 07+(–7)=0
This property holds true for all real numbers. For any number “a”, the additive inverse is “–a”. It is one of the key properties of addition in arithmetic and algebra. For example:
- The additive inverse of 3 is –3
- The additive inverse of –5 is 5
- The additive inverse of 0 is 0
This property is important in solving equations, especially when isolating variables. If you are trying to eliminate a term from one side of an equation, you can add its additive inverse to both sides. This balances the equation and simplifies solving.
Also, note that the additive inverse is different from the multiplicative inverse, which involves reciprocals (for example, the multiplicative inverse of 7 is 1⁄7 because 7 × 1⁄7 = 1).
Among the choices given:
- a) 7 is the number itself, not its inverse
- b) –7 is correct
- c) 0 is neutral, not the inverse of 7
- d) 1 is the multiplicative identity, not the additive inverse
Final answer: b) –7
