Question

a) Write additive inverse of $\dfrac{2}{8}$ and $\dfrac{{ - 6}}{{ - 5}}$.
b) write multiplicative inverse of -13 and $\dfrac{{ - 13}}{{19}}$

Answer 1

Hint: The various operations such as addition, subtraction, division and multiplication have their own properties. Inverse is the reciprocal of the number basically, we have to find the additive and multiplicative inverse for the following numbers.

Complete step-by-step answer:
Additive inverse is simply when both the number and its additive inverse is added they give the sum as zero, that is we can conclude that the additive inverse of the number is equal to the number in terms of magnitude but differs only in the terms of sign. Therefore a positive number will always have a negative number as its additive inverse and a negative number will have a positive additive inverse.
Now let us find the additive inverse for the given numbers,
Additive inverse of $\dfrac{2}{8}$is given by= -$\dfrac{2}{8}$
As both on adding up results in zero ($\dfrac{2}{8}$-$\dfrac{2}{8}$=0)
Additive inverse of $\dfrac{{ - 6}}{{ - 5}}$is given by=$ - \dfrac{6}{5}$
We must not get confused as the number $\dfrac{{ - 6}}{{ - 5}}$is a negative number but its negative sign will get cancelled from both numerator and denominator making it a positive number.
b) let us understand multiplicative inverse for the second part of the question, a multiplicative inverse of the number when multiplied with the same number must give the product as 1 that is both the numbers must be reciprocal of each other such that the cancel up to give 1 as a product.
Now let us find multiplicative inverse of the given numbers,
Multiplicative inverse of -13 is given by=$ - 13 \times \dfrac{1}{{ - 13}} = 1$
Multiplicative inverse of $\dfrac{{ - 13}}{{19}}$ is given by=$\dfrac{{ - 13}}{{19}} \times \dfrac{{19}}{{ - 13}} = 1$

Note: Therefore we can generalize the multiplicative inverse of a number x by 1/x. since multiplying x with its multiplicative inverse will give 1.unlike additive inverse multiplicative inverse has the same sign as its number. The order and the grouping property is valid for both multiplication and addition.