About Multiplication of Integers
What is Multiplication of Integers?
Multiplication of integers is the process of repetitive addition of numbers, in which a number is added to itself a specific number of times. For example, 5 x 3 = 15, which means the number 5 has been added 3 times. Multiplication helps us to do bigger calculations faster and easier.
Rules of Multiplication
1. Integers with the same signs: If two integers have the same sign, their product will be positive, irrespective of their sign.
Examples:
a. 3 x 4 = 12 (positive)
b. -6 x -8 = 48 (positive)
2. Integers with different signs: If two integers have different signs, positive and negative or negative and positive, their product will be negative.
Example:
a. 7 x -2 = -14 (negative)
[Note: Any number multiplied by 0 results in 0 and any number multiplied by 1 results in the same number.]
Rapid Recall
Solved Examples
Example 1: Henry wants to distribute donuts to his friends on his birthday. If he has nine friends, how many doughnuts will Henry need to buy so that each one gets three donuts?
Solution:
As stated in the question, Henry wants to distribute 3 donuts to 9 of his friends.
Let ‘n’ be the number of donuts that Henry needs to buy.
So, to find ‘n’, we need to multiply the number of friends with the number of donuts that each should get.
That is,
n = 3 x 9
n = 27
Therefore, the number of donuts that Henry needs to buy for his nine friends is 27.
Example 2: Find the product of the following numbers and mention whether it is a positive or negative integer.
a) -5 x -9
b) 4 x –8
c) 7 x 10
Solution:
a) -5 x -9 = 45
Here, the result is a positive integer as both integers to be multiplied have the same sign.
b) 4 x –8 = -32
Here, the result is a negative integer as both integers to be multiplied have different signs.
c) 7 x 10 = 70
Here, the result is a positive integer as both integers to be multiplied have the same sign.
Example 3: “The product of three positive integers is always positive”. Check whether the given statement is true with the help of an example.
Solution:
Let’s take three positive integers, say a = 9, b = 5 and c = 4; let’s multiply them.
9 x 5 x 4 = 45 x 4 [Multiply 9 with 5]
= 180 [Multiply 45 with 4]
The result is positive as all three numbers have the same sign, that is, positive. Therefore, the given statement is true.
The two rules of multiplication of integers are:
- Integers with the same sign give positive results.
- Integers with the different signs give negative results.
Any number multiplied by zero gives zero. So, 45 x 0 equals 0.
We use multiplication in many instances like counting the population of a city, calculating the annual income of an organization, total number of items in a store and so on.
When a negative number is multiplied by a negative number, the sign of the product will be positive.