Operations of Integers

Operations of Integers on A Number Line

Hope you are familiar with the number line given below. Traditionally, the number zero is placed in the center of the number line. When we extend to the right of zero we have positive numbers and the negative numbers extend to the left of zero. In order to add positive integers and negative integers, we will imagine that we move along a number line. We are going to discuss about addition and subtraction of integers on number line, addition and subtraction of integers on number line.

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  1. Addition of Integers using Number Line-

Let’s take a few examples for better understanding of addition of integers using number line -

For example :
Example 1) If suppose we are asked to add  the numbers 4 and 3, we would start by moving to the number 4 present on the number line -- exactly move four units to the right of zero. Then we have to move three units to the right. Since we landed up seven units to the right of zero, we say that the sum of 3 and 4 is 7.

Example 2) If  suppose we are asked to add the numbers 8 and -2, we would start by moving eight units to the right of zero and then we would move two units left from there as we know that negative numbers make us move to the left side of the number line. Since our last position is six units to the right of zero, we can say that the sum of 8 and -2 is 6.


Here are the rules that you need to keep in mind in Addition of integers using number line-

Addition of Integers Using Number Line –

Positive Integer + Positive Integer =

Positive Integer

Negative Integer + Negative Integer =

Negative Integer

Positive Integer + Negative Integer =

Use the sign of the larger number, Subtract

Negative Integer + Positive Integer =

Use the sign of the larger number, Substract

 

  1. Subtraction of Integers on Number Line-

We will learn how to transform the subtraction problems into addition problems. Let’s discuss in details the subtraction of Integers on number line. Adding and subtracting integers using a number line are quite related.

 The technique for changing subtraction problems into addition problems is quite simple. There are two steps you need to keep in mind:

Step 1) Change the subtraction sign in the given question into an addition sign.

Step 2) Take the opposite of the number that immediately follows the newly placed addition sign.

 Now let's take a look at example number 1:

Example 1) 3 - 4

 According to the steps that we have discussed above, we have to change the subtraction sign to an addition sign in any question. We need to take the opposite of 4, which is -4. Therefore now the problem becomes:

3 + (-4) Now using the rules for addition, the answer we get is equal to -1.

 Here are a few other examples for better understanding:

 Example 2) -2 – 7 =    -2 + (-7) = -9

 Example 3) 6 - (-2) = 6 + 2 = 8

 Example 4) -7 - (-2) = -7 + 2 = -5

Subtraction of integers on number line

Negative number - Positive number gives us =

Negative Number

Negative number - Negative number gives us =

Negative Number + Positive number

Positive number - Negative number gives us =

Positive number

 

  1. Multiplication of Integers on number line-

Now we have to understand the rules of multiplication.The first rule is very easy to remember because we have been learning it for a very long time. When we work with positive numbers under multiplication it always yields positive answers. However, the last three rules are a bit more challenging to understand, here are the rules.


The second and third steps can be explained at the same time. This is because we can multiply numbers in any order. -7 x 3 has the same answer as 3 x -7, which is always true for all integers in Mathematics. (This property has a special name in mathematics which is known as the commutative property.) We can say thus that the second and third rules are equivalent.


Positive number × Positive number=

Positive number

Negative number × Negative number=

Positive number

Negative number × Positive number =

Negative number

Positive number × Negative number= 

Negative number


  1. Division of Integers on number line-

The rules for division are exactly the same as those for the rules of multiplication. If suppose you take the rules for multiplication and change the multiplication signs to division signs, then we would have an accurate set of rules for division.

Here are three examples given below:

    Example 1)   -27 ÷ 3 = -9

    Example 2)    24 ÷ (-4) = -6

    Example 3)   -21 ÷ (-3) = 7

Positive number / Positive number=

Positive number

Negative number / Negative number=

Positive number

Negative number / Positive number =

Negative number

Positive number × Negative number= 

Negative number

Questions to be solved –

Question 1) Find the sum of the integers +25 and -5.

Solution) When we find the sum of integers +25 and -5 , we need to subtract the two numbers (25-5) = +20

Question 2) Divide the integers -27 and 3.

Solution) When we need to divide the two integers -27 and 3, on dividing we get the value as -9.

FAQ (Frequently Asked Questions)

1. What are the rules for integers and how do I multiply integers?

When we have to add any two given integers having the same sign, keep the same sign and add the absolute value of each number to get the sum. If we want to add integers with different signs, we keep the sign of the number with the largest absolute value and just subtract the smallest absolute value from the largest value. Subtract an integer by adding its opposite.

When you have to multiply any two integers having the same signs, the result is always positive. You just need to multiply the absolute values and make the answer positive. When you multiply two integers with different signs, the result you will get will always be negative. You need to just multiply the absolute values and make the answer a negative.


2. What are the four rules of integers and what is the product of an integer and 1?

Integers are whole numbers, both positive and negative numbers. You can perform four basic math operations on the integers: addition, subtraction, multiplication, and division. Addition of integers using the number line, remember that negative integers move you to the left on the number line and positive integers move to the right on the number line . Adding and subtracting integers using a number line are quite related.We know that the product of any two integers with unlike signs will always give a negative integer. Therefore, the product of the integers with unlike signs suppose +3 and −1 is: (+3)×(−1)=−(3×1) = −3 which is a negative integer.