Question

The product of the additive inverse and the multiplicative inverse of

the integer (-56) is with explanation​

Answer 1

Answer:

The answer is -1

Step-by-step explanation:

The additive inverse of -56=56

The multiplicative inverse of -56= -1/56

Therefore,their product= 56×(-1/56)= -1

HOPE THIS HELPS!!

Answer 2

Answer:

The product of the additive inverse and multiplicative inverse of -56 is -1

Step-by-step explanation:

let consider the additive inverse,

Definition:

Additive inverse of a number, is the negation of that particular number or a number added to that number, which gives additive identity 0 such that, addition is the standard addition operation.

To find the additive inverse of a -56,

Let x be the additive inverse of the -56 then,

(-56)+x=0 implies

(-56)+x+56=0+56 (add 56 in LHS and RHS of the equation)

Rearranging the equation we have,

56-56+x=56 subtracting a number from same number is zero that is, 0+x=56

x=56.

Therefore, the additive inverse of -56 is 56 when addition is standard addition operation.

On considering the multiplicative inverse,

Definition:

Multiplicative inverse of a number is another number when multiplied  gives multiplicative identity 1,when multiplication is standard multiplication.

To find the To find the multiplicative inverse of  -56,

Let m be the multiplicative inverse,

then,

m×(-56)=1

multiply $\frac{1}{m}$ in both side of the equation we get,

m×(-56)×($\frac{1}{-56}$)=1×($\frac{1}{-56}$)

that is, m×($\frac{-56}{-56}$)=$\frac{-1}{56}$

implies m×1=$\frac{-1}{56}$, a number multiplying with multiplicative identity is that number itself

hence, m=$\frac{-1}{56}$

Therefore, the multiplicative inverse of -56 is $\frac{-1}{56}$ When multiplication is standard multiplication.

Then, the product of additive inverse and multiplicative inverse is

here, additive inverse of -56=56

multiplicative inverse of -56 = $\frac{-1}{56}$

then,

56 × $\frac{-1}{56}$ =$\frac{-56}{56}$= -1.

Hence, we can conclude that the product of additive inverse and multiplicative inverse of -56 is -1.

In general, if an is the number then its additive inverse will be -a and the multiplicative inverse will be  $\frac{1}{a}$.(where, an is any real number other than o)

Hence, the product of additive inverse and multiplicative inverse of a number in general is also

-a× $\frac{1}{a}$= $\frac{-a}{a}$=-1.

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