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Properties of Subtraction of Integers

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Last updated date: 29th Feb 2024
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An Introduction to Subtraction of Integers

Subtracting integers is the process of finding the difference between two integers. It may result in an increase or a decrease in value, depending on whether the integers are positive or negative. We can subtract one integer from another. This is the easiest way.


We can also subtract the sum of two integers, which is also easy to do. But in many cases, we need to do subtraction operations involving more than two numbers. A negative number can be subtracted from a positive number or added to a positive number, for instance. In this article, we are going to learn about the subtraction of integers and their properties.

Subtraction of Integers


Subtraction of Integers

What are Integers?

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero. A few examples of integers are -5, 0, 1, 5, 8, 97, and 3,043.


Addition of Integers Definition

Adding integers is the process of finding the sum of two or more integers where the value might increase or decrease depending on the integer being positive or negative.

Example: Add the given integers: 2 + (-5)

Ans: Here, the absolute values of 2 and (-5) are 2 and 5, respectively.

Their difference (larger number - smaller number) is 5 - 2 = 3

Now, among 2 and 5, 5 is the larger number, and its original sign is “-”.

Hence, the result gets a negative sign, "-”.

Therefore, 2 + (-5) = -3


Subtraction of Integers Definition

The subtraction of integers is an arithmetic operation performed on integers with the same sign or with different signs to find the difference.


Subtraction of Integers


Subtraction of Integers


Example: Subtract the given integers: 7 - 10

Ans: 7 - 10 can be written as (+ 7) - (+)10

Convert the given expression into an addition problem and change the sign of the subtrahend, so, we get: 7 + (-10)

Here, the absolute values of 7 and (-10) are 7 and 10, respectively.

Their difference (larger number - smaller number) is 10 - 7 = 3.

Now, among 7 and 10, 10 is the larger number, and its original sign is “-”.

Hence, the result gets a negative sign, "-”.

Therefore, 7 - 10 = -3


Properties of Addition and Subtraction of Integers

This section will be about the properties of addition and subtraction of integers. We will discuss the following properties:

  • If we subtract 0 from any integer, the answer will be the integer itself.

Example: 15 - 0 = 15

  • If we subtract any integer from 0, we will find the additive inverse or the opposite of the integer.

Example: 0 - 15 = -15

  • Subtraction of integers is done by changing the sign of the subtrahend. After this step, if both numbers are of the same sign, then we add the absolute values and attach the common sign. If both the numbers are of different signs, then we find the difference between the absolute numbers and place the sign of the bigger number in the result.

Example: (-1) - (-6) = -1 + 6 = 5

  • For addition: When both integers have the same signs, add the absolute values of integers, and give the same sign as that of the given integers to the result.

Example: 5 + 2 = 7

  • For addition: When one integer is positive and the other is negative, find the difference between the absolute values of the numbers and then give the sign of the larger of these numbers to the result.

Example: 2 + (-5) = -3


The principles for subtracting integers are displayed in the table below along with examples.


Properties of Addition and Subtraction of Integers


Properties of Addition and Subtraction of Integers


Properties of Addition and Subtraction of Integers Related Solved Examples

Q1. Solve: -90 - (-56)

Ans: This question is based on subtracting two integers with the same sign.

From the question, we have -90 - (-56).

This can be written as -90 + 56.

Let us find the difference between the absolute values.

So, 90 - 56 is 34. Since 90 > 56, the answer sign will be the same as the sign of 90 which is negative.

Therefore, -90 - (-56) = -34.


Q2. Subtract -7 from -12 using the rules of subtracting integers.

Ans: This question is based on subtracting integers with the same sign. Here, we have to subtract two integers with the same sign, -12 and -7.

-12 - (-7) = -12 + 7

= -5

Therefore, the difference between -12 and -7 is -5.


Q3. Add the given integers: (-2) + 5

Ans: Here, the absolute values of (-2) and 5 are 2 and 5, respectively.

Their difference (larger number - smaller number) is 5 - 2 = 3.

Now, among 2 and 5, 5 is the larger number, and its original sign is “+”.

Hence, the result will be a positive value. Therefore,(-2) + 5 = 3


Q4. Add the following integers: (-9) + (-5)

Ans: According to the rules of integers in addition, when both the integers have the same signs, we add the absolute values of integers and give the same sign as that of the given integers to the result.

The absolute values of the given integers are 9 and 5.

So we will add 9 + 5 = 14 and the sign of the sum will be negative.

Therefore, (-9) + (-5) = -14


Properties of Addition and Subtraction of Integers Worksheet

Here is a worksheet based on the property of addition and subtraction of integers, which will help in increasing the maths confidence of students.

Q1. $-10-(-6)=$ Ans: -4

Q2. $18-(2)=$ Ans: 16

Q3. $-20+15=$ Ans: -5

Q4. $-13+(-10)=$ Ans: -23

Q5. $18+(-17)=$ Ans: 1


Summary

In this article, we have learned about the addition and subtraction of integers. Here, we have seen how by using certain properties we can easily solve problems based on addition and subtraction. As for subtraction, we have to check the sign and then solve it. By applying the rules, it can be solved easily. The same thing can be done while solving the addition of integers. At the end of the article, we have added some solved examples and practice problems to have command over the topic.

FAQs on Properties of Subtraction of Integers

1. What are the characteristics of subtraction?

Subtraction has three properties:

  • Subtraction has the identity property.

  • Subtraction's order property.

  • The property of subtracting a number by itself.

2. What three components makeup subtraction?

The components of a subtraction issue are the minuend, subtrahend, and difference. In the subtraction problem, 16 – 7 = 9, the number 16  is the minuend, the number 7  is the subtrahend and the number 9  is the difference.

3. What is minuend and subtrahend?

The number being subtracted from is formally referred to as the minuend, while the number being subtracted is known as the subtrahend. The distinction is the outcome.