Answer:
Additive inverse of 19/-6 is 19/6
Additive inverse of -2/3 is 2/3
Multiplicative inverse of 19/-6 is -6/19
Multiplicative inverse of -2/3 is 3/-2 (also written as -3/2)
Step-by-step explanation:
(a) The additive inverse of a number is that number that when added to it gives 0.
For example, the additive inverse of x is -x.
This is because adding -x to x gives 0. i.e
x + (-x) = 0
In other words, the additive inverse of a number is the negative of that number.
Given:
(i) 19/-6
The additive inverse of 19/-6 is the negative of 19/-6 which is -(19/-6).
-(19/-6) then gives 19/6
Therefore, the additive inverse of 19/-6 is 19/6
(ii) -2/3
The additive inverse of -2/3 is the negative of -2/3 which is -(-2/3).
-(-2/3) then gives 2/3
Therefore, the additive inverse of -2/3 is 2/3
(b) The multiplicative inverse of a number is that number that when multiplied by it gives 1.
For example, the multiplicative inverse of y is 1/y.
This is because multiplying y by 1/y gives 1. i.e
y x (1/y) = 1
In other words, the multiplicative inverse of a number is the reciprocal of that number.
Given:
(i) 19/-6
The multiplicative inverse of 19/-6 is the reciprocal of 19/-6 which is 1/(19/-6).
1 / (19/-6) then gives -6/19
This is found by just swapping the numerator(19) and the denominator(-6)
Therefore, the multiplicative inverse of 19/-6 is -6/19
(ii) -2/3
The multiplicative inverse of -2/3 is the reciprocal of -2/3 which is 1/(-2/3).
1 / ( -2/3) then gives 3/-2
This is found by just swapping the numerator(-2) and the denominator(3)
Therefore, the multiplicative inverse of -2/3 is 3/-2 (also written as -3/2).
