Determine the integer whose product with (-1) is: -22

Hint: We use the definition of an integer and use the fact that a negative number multiplied with a positive number gives the product as a negative number. Assume the integer as a variable and form an equation of multiplication in the left hand side and write the value -22 in the right hand side of the equation.
* Set of integers contains all the positive numbers, all negative numbers and 0. It is usually denoted by Z. We can write the elements of a set of integers as \[Z = \left\{ {... - 3, - 2, - 2,0,1,2,3...} \right\}\]

Complete step-by-step solution:
We are given that the product of integers with (-1) is -22 and we have to find that integer.
Let us assume the integer as ‘x’
We can form an equation where the product of integers and (-1) is in the left side and -22 is in the right hand side of the equation.
\[ \Rightarrow ( - 1) \times x = - 22\]
To obtain the value of integer i.e. ‘x’ we divide both sides by such a number such that the left side has only ‘x’ left.
Divide both sides of the equation by -1
\[ \Rightarrow \dfrac{{( - 1) \times x}}{{( - 1)}} = \dfrac{{ - 22}}{{( - 1)}}\]
We can write the above equation as
\[ \Rightarrow \dfrac{{( - 1) \times x}}{{( - 1)}} = \dfrac{{22 \times ( - 1)}}{{( - 1)}}\]
Cancel same factors from numerators and denominator on both sides of the equation
\[ \Rightarrow x = 22\]
We check if the value obtained is integer or not if it lies in the set of integers i.e.\[Z = \left\{ {... - 3, - 2, - 2,0,1,2,3...} \right\}\].
Since 22 lies in Z, so 22 is an integer.

\[\therefore \]The value of integer is 22.

Note: Many students make the mistake of writing the answer as a rational number i.e. of the form \[p/q\] which is wrong, keep in mind integers do not contain rational numbers, they contain only negative numbers, 0 and positive numbers.