Question

Determine the integer whose product with (-1) is: a) -12 b) 35 *​

Answer 1

Step-by-step explanation:

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={...−3,−2,−2,0,1,2,3...}

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.

⇒(−1)×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

⇒(−1)×x(−1)=−22(−1)

We can write the above equation as

⇒(−1)×x(−1)=22×(−1)(−1)

Cancel same factors from numerators and denominator on both sides of the equation

⇒x=22

We check if the value obtained is integer or not if it lies in the set of integers i.e.Z={...−3,−2,−2,0,1,2,3...}

.

Since 22 lies in Z, so 22 is an integer.

∴

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.

Answer 2

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