Multiplication Of Integers

Multiplication of two integers is the repeated addition.

Example

  • 3 \times (-2) = three \ times \ (-2) = (-2) + (-2) + (-2) = - 6
  • 3 \times 2 =  three \ times \ 2 = 2 + 2 + 2 = 6

Now let’s see how to do the multiplication of integers without the number line.

1. Multiplication of a Positive Integer and a Negative Integer

To multiply a positive integer with a negative integer, we can multiply them as a whole number and then put the negative sign before their product.

So the product of a negative and a positive integer will always be a negative integer.

For two integers p and q, 

p \times (-q) = (-p) \times q = - (p \times q) = - pq

Example

4 \times (-10) = (- 4) \times 10 = - (4 \times 10) = - 40

2. Multiplication of Two Negative Integers

To multiply two negative integers, we can multiply them as a whole number and then put the positive sign before their product.

Hence, if we multiply two negative integers then the result will always be a positive integer.

For two integers p and q,

(-p) \times (-q) = (-p) \times (-q) = p \times q

Example

(-10) \times (-3) = 30

3. The Product of Three or More Negative Integers

It depends upon the number of negative integers.

a. If we multiply two negative integers then their product will be positive integer

(-3) \times (-7) = 21

b. If we multiply three negative integers then their product will be negative integer

(-3) \times (-7) \times (-10) = -210

If we multiply four negative integers then their product will be positive integer

(-3) \times (-7) \times (-10) \times (-2) = 420

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