Multiplication And Division Of Integers


About

Integers are a bigger collection of numbers which is formed by whole numbers and their negatives.

Multiplication

Multiplying a  positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer.

For example, – 2 × 5 = – 10 and – 3 × – 7 = 21.

Product of even number of negative integers is positive, whereas the product of odd number of negative integers is negative.

Division

When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.

Division of a negative integer by another negative integer gives a positive integer as quotient.

Rules to Remember:

  • Positive ÷ positive = positive
  • Negative ÷ negative = positive
  • Positive ÷ negative = negative
  • Negative ÷ positive = negative

Demonstration

Examples :

3 * (−7)=−21

3 times 7 equal 21. Since there is one positive and one negative number, the product is negative 21.

(−3)* (−7)=21

Now we have two negative numbers, so the result is positive.

Turning to division, you may recall that you can confirm the answer you get by multiplying the quotient by the denominator. If you answer is correct then the product of these two numbers should be the same as the numerator. For example,

15 / 5=3

In order to check whether 3 is the correct answer, we multiply 5 (the denominator) by 3 (the quotient):

5* 3=12

What happens when you divide two negative numbers? For example,

(−15)/(−5)=?

For the denominator (-5) to become the numerator (-15), you would have to multiply it by 3, therefore the quotient is 3.

So, the quotient of a negative and a positive number is negative and, correspondingly, the quotient of a positive and a negative number is also negative. We arrive at

(-15)/(-5)= 3