Content Writer
Addition and subtraction of integers are the most common arithmetic operations that are used to increase or decrease a number. Integers are a set of numbers that include all the non-fractional numbers, such as the positive number, negative number, and zero.
- Addition and subtraction of integers involve putting addition and subtraction operators in between.
- Adding two positive integers will result in positive integers.
- On the other hand, adding two negative integers results in the sum with a negative sign.
- When two different signed integers are added, that will result in subtraction only.
- The sign of the result will be the same as the larger number.
- In order to add and subtract signed integers, we can also make use of the number line.
- For example- [- . . . . . .-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,. . . . . . . . ] is a set of integers.
Key Terms: Addition and Subtraction of Integers, Integers, Arithmetic Operation, Addition, Subtraction, Fraction, Positive Numbers, Rules for Addition or Subtraction, Multiplication of Integers
Addition and Subtraction
[Click Here for Sample Questions]
Addition and subtraction are the two primary arithmetic operations in Maths. However, apart from these two operations, multiplication and division are also two primary operations.
- Addition involves the summation of two or more numbers, giving the total value of the numbers.
- On the other hand, the operation of subtraction is the opposite of addition.
- Subtraction involves the reduction of two or more numbers, giving the reduced value of the numbers.
- Addition and subtraction are also used for rational and irrational numbers.
- For this reason, both operations are applicable to all real and complex numbers.
- Addition is denoted by + sign, and subtraction is denoted by – sign.
- Also, while performing algebraic operations, the addition and subtraction algebraic expressions are done based on the same rules.
Example of Addition and SubtractionExample: For instance, if a basket has six mangoes, and if we add 2 more mangoes to it, there will be eight mangoes in total. Likewise, if there are six mangoes in a basket and we take two mangoes out of it, then the basket will be left with four mangoes, which shows subtraction. |
Addition and Subtraction of Integers
Read More:
| Chapter Related Concepts | ||
|---|---|---|
| Polynomials | Quadratic Equations Formula | Degree of polynomial |
| Distance Formula | Section Formula | Arithmetic |
Rules for Addition and Subtraction
[Click Here for Sample Questions]
Integers include all the numbers from a number line except the fractional numbers. Talking about the rules and regulations, it is the same in the case of natural numbers as well as integers.
- The addition of two numbers involves addend + addend = sum.
- Subtraction of two numbers involves minuend - subtrahend = difference.
- Addition and subtraction of integers include positive and negative signs.
- The rules are divided into three categories.
Negative Sign and Positive Sign
The integers which we add or subtract can be positive or negative. Therefore, it is important to know the rules for positive and negative symbols.
- Positive sign/symbol: (+)
- Negative sign/symbol: (-)
Rules for Addition of Integers
Different conditions under which we perform the addition operation are as follows:
Addition of two Positive Numbers
In this case two integers are positive and they are put under addition operation. The result is a positive value, just like the addition of whole numbers.
(+a)+(+b) = (a+b)
Example of Addition of two Positive NumbersExample: 3+5 = 8 |
Addition of Negative Numbers
When two integers are of negative sign, and they need to be added. In that case, add both the numbers and put a negative sign in front of it.
(-a)+(-b) = -(a+b)
Example of Addition of Negative NumbersExample: (-3)+(-4)=(-7) |
Addition of one Positive and one Negative Number
If you have one integer that is positive and another one that is negative, then take the difference between the numbers and put the sign of the greater number.
(a+(-b)) = (a-b)
Example of Addition of one Positive and One Negative NumberExample: 4+(-6)=(-2) |
Addition of Integers
The rules of addition of integers are tabulated below:
| Types of Numbers | Operation Applied | Final Result | Example |
|---|---|---|---|
| ( + ) + ( + ) | Addition | Positive ( + ) | 9 + 8 = 17 |
| ( - ) + ( - ) | Addition | Negative ( - ) | (- 4 ) + (- 5 ) = (- 9) |
| ( - ) + ( + ) | Subtraction | Positive ( + ) | ( - 2 ) + ( 8 ) = 6 |
| ( + ) + ( - ) | Subtraction | Negative ( - ) | ( 8 ) + ( - 10 ) = (- 2) |
Rules for Subtraction of Integers
The different conditions under which the subtraction operation takes place-
Subtraction of two Positive Numbers
In this case, two integers are positive, and they are put under subtraction operation. The result is a positive or negative value, just like the subtraction of whole numbers.
(+a)-(+b)=a + (-b)
Example of Subtraction of two Positive NumbersExample: 3-6=-3 |
Subtraction of two Negative Numbers
If both the integers are negative, they need to go under subtraction. In that case, subtract both the numbers and put the sign of the greater number.
(-a)-(-b)= -a + (+b)
Example of Subtraction of two Negative NumbersExample: (-2)-(-7)= 5 |
Subtraction of one Positive and one Negative Number
When one of the integers is positive, and the other is negative, both integers are subtracted. It involves the addition of two numbers and reversing the sign of two numbers with a subtraction sign.
a-(-b)=a + (+b) or -a-(+b) =-a + (-b)
Example of Subtraction of one Positive and one Negative NumberExample: 4-(-7)= 11 |
Subtraction of Integers
The rules for subtraction of integers are tabulated below:
| Types of Numbers | Operation Applied | Final Result | Example |
|---|---|---|---|
| ( + ) - ( + ) | Subtraction | Positive / Negative | 9 - 8 = 1 |
| ( - ) - ( - ) | Subtraction | Negative / Positive | (- 4 ) - (- 5 ) = 1 |
| ( - ) - ( + ) | Subtraction | Negative ( - ) | ( - 2 ) - ( 8 ) = (-10) |
| ( + ) - ( - ) | Addition | Positive ( + ) | ( 8 ) - ( - 10 ) = (18 ) |
Properties of Addition and Subtraction
[Click Here for Sample Questions]
The properties of addition and subtraction is divided into two categories which are as follows:
Properties of Addition
The properties of addition are as follows:
Closure Property
Closure Property involves addition of two integers is an integer.
Commutative Property
If we have two numbers, a and b, then the total of any two integers is the same even if their order of addition is changed.
Associative Property
If we have three numbers, a, b and c, then the total of any three integers is the same even if their order of addition is changed.
Additive Integer
It involves the addition of an integer with zero, which will give an integer as an answer.
Properties of Subtraction
The propertoes of subtraction are as follows:
Closure Property
The subtraction of two integers is an integer.
Commutative Property
If we have two numbers, a and b, then the total of any two integers is the same even if their order of subtraction is changed. This is commutative property.
Associative Property
If we have three numbers, a, b and c, then the total of any three integers is the same even if their order of subtraction is changed.
Multiplication of Integers
[Click Here for Sample Questions]
The sign of the resulting integer depends on the sign of the largest value in addition and subtraction.
Example of Multiplication of IntegersExample: -7+4 = -3, but in the case of the multiplication of integers, two signs are multiplied together. |
The rules of multiplication of integers are as follows:
| (+) × (+) = + | Plus x Plus = Plus |
| (+) x (-) = – | Plus x Minus = Minus |
| (-) × (+) = – | Minus x Plus = Minus |
| (-) × (-) = + | Minus x Minus = Plus |
Read More:
| Class 9 Maths Related Concept | ||
|---|---|---|
| Prime Numbers | Descending Order | Real Numbers Formula |
| Natural numbers | Number Lines | Division of rational expression |
Things To Remember
- Addition and subtraction of integers are fundamental operations of mathematics.
- The sign of the addition operation is +, and the sign of the subtraction operation is -.
- The addition of two numbers gives the sum of two numbers.
- Subtraction of two numbers determines the difference between two numbers.
- In addition, negative and positive signs play an important role, so you need to be careful while doing the operations.
- Make sure that you follow all the basic rules and regulations discussed above in the article to avoid any confusion and wrong answers.
Sample Questions
Ques: Evaluate the following terms: (3 marks)
- 11 + 15
- ( - 8 ) - ( 13 )
- ( + 34 ) + ( - 29 )
Ans: The process is as follows:
- We have been given-
- 11 + 15
- It is a simple addition of positive integers same as the natural numbers.
- 26
- We have been given-
- ( - 8 ) - ( 13 )
- Here, we are provided with a negative operation, but we can notice that the integer after the operation has a positive sign.
- We have to resolve the signs first. When a negative number is multiplied by a positive one, we get a negative value.
- - 8 - 13
- Now, we have two integers having the same signs. So, we need to add them and the sign of the resultant value will also be negative.
- - 21
- We have been given-
- ( + 34 ) + ( - 29 )
- Here, we have an additional operation, but we can notice that the integer after the operation has a negative sign. So, we need to solve the signs first. When a positive number is multiplied by a negative one, we get a negative value.
- 34 - 29 [Positive x Negative = Negative]
- We can see that now it has turned out to be the simplest subtraction method.
- 5
Ques: Evaluate the following: (2 marks)
- (- 8 ) + 9
- (-1) – ( -5)
Ans: The process is as follows:
- We have been provided the equation-
- (- 8 ) + 9
- - 8 + 9
Here, we have a positive integer and one negative integer. So, all we need to do is to subtract both of them. The resultant value will have a positive sign because the greater number has a positive sign.
- 1
- We have been provided with the equation-
- (-1) - (-5)
Here, we can see that the operation is subtraction, but after the operation sign, there is a negative integer. So, we need to first solve both the signs.
- (-1) + 5 [Negative x Negative = Negative]
Now, we are left with one negative and another positive integer so we have to do subtraction. The sign of the resultant value will be positive because the greater number, which is 5, has the positive sign.
- 4
Ques: Add -54 and 60. (2 marks)
Ans: We need to add (-54) and 60
Then, we can write it as-
(-54) + 60
Here we have one negative integer and one positive integer. Now, even if the original operation says to do addition, we have to do subtraction because these two terms have different signs i.e., positive and negative.
= -54 + 60 = 6
Ques: Subtract -50 from -67. (2 marks)
Ans: We need to subtract (-50) from (-67). So, we can write it as-
(-67) - (-50)
We have come across a negative-negative sign encounter, and we all know that Negative x Negative = Positive. So, we will get-
= (-67) + 50
= -67 + 50
The resultant value will have a negative sign because the greater number out of the two has a negative sign.
Ques: Find the difference between 70 and 54. (2 marks)
Ans: We have been asked to find the difference between 70 and 54.
When we have been asked to find the difference, it means that we need to subtract the smaller number from the greater one. So, we will get the equation as-
70 - 54 = 16
Ques: Imagine you leave for the stationery shop with 100 bucks in your pocket, and you need to buy some things for your new project. You buy a pencil worth 5 bucks, a chart paper worth 10 bucks, some colors worth 30 bucks, and some other stuff worth 20 bucks. How much money is left in your pocket. (4 marks)
Ans: Money in the pocket initially = 100
Bought a pencil worth = 5
Bought chart paper worth = 10
Bought colors worth = 30
Bought other stuff worth = 20
Money left in the pocket = 100 - 5 - 10 - 30 - 20
Here, we will assign the money spent with a negative sign because they are benignly taken out being spent.
First, we will add all the negative integers. So, we will get-
= 100 - 65
= 35
So, you will leave with 35 bucks in your pocket after spending all the money.
Ques: Evaluate (- 40) + 10 - (-54) + 80 - (+60) + (-32). (3 marks)
Ans: We have been given-
(- 40) + 10 - (-54) + 80 - (+60) + (-32)
= (- 40) + 10 - (-54) + 80 - (+60) + (-32)
= - 40 + 10 + 54 + 80 - 60 - 32
Now, we need to add all the like terms and simplify it.
= -132 + 144
= 12
Ques: A plane is flying at the height of 3500 feet above sea level. A point comes when it is exactly above a submarine that is 500 feet below sea level. Find the vertical distance between them. (3 marks)
Ans: The height at which the plane is flying = 3500 feet.
The depth of the submarine = -500 feet
We will take the distance of the submarine from the sea level as negative because it is below sea level.
Now we need to subtract both the integers so that we can get the right vertical distance.
= 3500 -(-500)
= 3500 + 500
= 4000 feet
Therefore, the vertical distance between the airplane and the submarine is 4000 feet.
Ques: Selena bought 16 chocolates. She ate 6 and gave 3 to her mom. How many chocolates does she have left. (2 marks)
Ans: She ate 6 chocolates so,
- 16-6=10,
- She gave 3 to her mom, now
- 10-3= 7
- Selena has 7 chocolates left with her.
Ques: John daily travels 3 km on rickshaw and 6 km by bus. Then he walks 750m to school. How much distance does he travel to reach school. (2 marks)
Ans: Total distance travelled= distance travelled by rickshaw distance travelled by bus distance travelled on foot
Total distance= 3 + 6 + 0.75 (750 m converted to km)
Ans- 9.75 kms
Ques: Rachel goes to the market and buys groceries of 300 and clothes of 400 and has a pastry for 60. How much did she spend in total. (2 marks)
Ans: Total money spent= cost of groceries + cost of clothes + cost of pastry
300 + 400 + 60 = 760.
Rachel spent 760 on shopping.
Read Also:
Comments