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3 years ago

Write additive and multiplicative inverse of19/-6 and-2/3

Mathematics

1 answer:

Sedbober [7]3 years ago

4 0

<h2>Answer:</h2>

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)

<h2>Step-by-step explanation:</h2>

(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 <em>negative</em> 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 <em><u>negative</u></em> 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 <em>reciprocal</em> 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 <em>reciprocal</em> 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).

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Write additive and multiplicative inverse of19/-6 and-2/3​

Write additive and multiplicative inverse of19/-6 and-2/3