Find the Additive Inverse of: −7/9
Any number that can bring the entire result to zero is an additive inverse. In other words, when a number is multiplied by its additive inverse, the result is zero. If we take the number 1 and multiply it by -1, the outcome is zero. As a result, 1’s additive inverse is -1.
Even in actual life, everything we perceive can be reduced to zero if the exact inverse is discovered. The correct amount of fire and ice, for example, will cancel each other out and the outcome will be zero.
The value of an additive inverse of a number is defined as the value that when added to the original number yields zero. It’s the amount we add to a number to make it equal zero.
If x is an original number, then its additive inverse is minus x, or -x, as follows:
x + (-x) = x – x = 0
Hence, Additive inverse of x is -x.
Now, in case of -x i.e. the additive inverse of -x must be x or positive as follows:
(-x) + x = -x + x = 0
Examples of Additive Inverse
- The additive inverse of 3 is -3. (Since, 3 + (-3) = 0)
- The additive inverse of 40 is -40. (Since, 40 + (-40) = 0)
- The additive inverse of 100 is 100, (Since, 100 + (-100) = 0)
- The additive inverse of -2431 is 2431. (Since, (-2431) + 2431 = 0)
Similarly, in case of fractions the additive inverse are given as:
If (p/q) is an original fraction, then its additive inverse is minus (p/q), or (-p/q), as follows:
p/q + (-p/q) = p/q – p/q = 0
Hence, Additive inverse of p/q is -p/q.
Now, in case of (-p/q) i.e. the additive inverse of (-p/q) must be (p/q) or positive as follows:
(-p/q) + p/q = -p/q + p/q = 0
Find the Additive Inverse of: −7/9
Solution:
The given fraction is -7/9.
As we know that, the additive inverse of any fraction is given as:
p/q + (-p/q) = p/q – p/q = 0
This implies, the additive inverse of p/q is -p/q.
Now, in case of (-p/q) i.e. the additive inverse of (-p/q) must be (p/q) or positive as follows:
(-p/q) + p/q = -p/q + p/q = 0
Similarly, the additive inverse of -7/9 is 7/9 as follows:
(-7/9) + 7/9 = 0
Hence, the additive inverse of -7/9 is 7/9 or positive 7/9.
Similar Questions
Question 1: What is the additive inverse of xy?
Answer:
The additive inverse of xy is -xy as follows:
xy + (-xy) = xy – xy = 0
Question 2: Is there a similarity between additive inverse and additive identity?
Answer:
No, they’re not the same. The additive inverse occurs when you add two numbers together to achieve a zero result. The value that is added to get the original integer, which is zero, is called additive identity.
Question 3: What is the additive inverse of 1/100?
Answer:
The additive inverse of 1/100 is -1/100 as follows:
1/100 + (-1/100) = 1/100 – 1/100 = 0
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