(i) For any integer $a$, what is $(-1)\times a$ equal to?
(ii) Determine the integer whose product with $(-1)$ is
(a) $-22$
(b) $37$
(c) $0$

To do:

We have to 

(i) Find $(-1)\times a$, for any integer $a$.

(ii) Determine the integer whose product with $(-1)$ is

(a) $-22$         

(b) $37$     

(c) $0$

Solution:

(i) For any integer $a$, $(-1)\times a$ is equal to $-a$ as shown below.

$( -1 )\times a=-a$                           [where $a$ is any integer]

(ii) 

(a) Let $x$ be the required integer

This implies,

$x \times (-1)=-22$

$-x=-22$

$x=22$

The integer whose product with $(-1)$ is $-22$ is $22$.

(b)

Let $x$ be the required integer.

This implies,

$x\times (-1)=37$

$-x=37$

$x=-37$

The integer whose product with $(-1)$ is $37$ is $-37$.

(c)

Let $x$ be the required integer.

This implies,

$x\times (-1)=0$

$-x=0$

$x=0$

The integer whose product with $(-1)$ is $0$ is $0$.