# Addition And Subtraction Of Integers

In addition and subtraction of integers, we will learn how to add and subtract integers with the same sign and different sign. We can also make use of number line to add and subtract signed integers. There are certain rules for integers that has to be followed to perform operations on them.

Adding two positive integers results in positive integers, whereas adding two negative integers will results in the sum with a negative sign. But, the addition of two different signed integers, will result in subtraction only. See few examples below:

• 2+2 = 4
• 2 + (-2) = 0
• -2 + (-2) = -4
• -2 – (-2) = 0

Addition and subtraction are two major arithmetic operations in Maths. Apart from these two operations, multiplication and division are also two major operations that we learn in basic Maths.

The addition represents the values added on the existing value. For example, a basket has two balls and if we add more than 2 balls to it, then there will be four balls in total. Similarly, If there are four balls in a basket and if we take out two balls out of it, then the basket is left with only two balls, which shows subtraction.

Addition and subtraction are not only used for integers but also for rational numbers and irrational numbers. Therefore, both the operations are applicable for all real numbers and complex numbers. Also, while performing algebraic operations, the addition and subtraction algebraic expressions are done based on the same rules.

## Rules to Add and Subtract

Integers are a special group of numbers that are positive, negative and zero, which are not fractions. Rules for addition and subtraction are the same for all.

### Negative Sign and Positive Sign

The integers which we add or subtract could be positive or negative.  Hence, it is necessary to know the rules for positive and negative symbols.

Positive sign/symbol: (+)

Negative sign/symbol: (-)

Addition of integers means there are three possibilities. They are:

• Addition between two positive numbers
• Addition between two negative numbers
• Addition between a positive number and a negative number
 Type of Numbers Operation Result Example Positive + Positive Add Positive (+) 10 + 15 = 25 Negative + Negative Add Negative (-) (-10) + (-15) = -25 Positive + Negative* Subtract Positive (+) (-10) + 15 =5 Negative + Positive* Subtract Negative (-) 10 + (-15)= -5

Whenever a positive number and a negative number are added, the sign of the greater number will decide the operation and sign of the result. In the above example 10 + (-15) = -5 and (-10) + 15 =5; here, without sign 15 is greater than 10 hence, numbers will be subtracted and the answer will give the sign of the greater number.

Also, since we know the multiplication of negative sign and a positive sign will result in negative sign, therefore if we write 10 + (-5), it means the ‘+’ sign here is multiplied by ‘-’ inside the bracket. Therefore, the result becomes 10 – 5 = 5.

Alternatively, to find the sum of a positive and a negative integer, take the absolute value (“absolute value” means to remove any negative sign of a number, and make the number positive) of each integer and then subtract these values. Take above example, 10 + (-15); absolute value of 10 is 10 and -15 is 15.

⇒ 10 – 15 = -5

Thus, we can conclude the above table as follow:

 Adding two positive integers results in positive integer Adding two negative integers results in sum of integers with a negative sign. Addition of a positive and a negative integer gives either a positive or negative-sum depending on the value of the given numbers.

Note: The sum of an integer and its opposite is always zero. (For example, -5 + 5= 0)

### Subtraction of Integers

Like in addition, the subtraction of integers also has three possibilities. They are:

• Subtraction between two positive numbers
• Subtraction between two negative numbers
• Subtraction between a positive number and a negative number

For ease of calculation, we need to renovate subtraction problems into addition problems. There are two steps to this:

1. After converting the sign, take the inverse of the number which comes after the sign.

Once the transformation is done, follow the rules of addition given above.

For example, find the value of: (-5) – (7)

⇒ (-5) + (7)

Step 2: Take the inverse of the number which comes after the sign

5 + (-7)                                  (opposite of 7 is -7)

5 + (-7) = -12      [Add and put the sign of greater number]

## Multiplication of Integers

In addition and subtraction, the sign of the resulted integer depends on the sign of the largest value. For example, -7+4 = -3 but in the case of multiplication of integers, two signs are multiplied together.

 (+) × (+) = + Plus x Plus = Plus (+) x (-) = – Plus x Minus = Minus (-) × (+) = – Minus x Plus = Minus (-) × (-) = + Minus x Minus = Plus

Rules:

• When two positive integers are multiplied then the result is positive.
• When two negative integers are multiplied then also the result is positive.
• But when one positive and one negative integer is multiplied, then the result is negative.
• When there is no symbol, then the integer is positive.

## Solved Examples

Example 1: Evaluate the following:

1. (-5 )+  9
2. (-1) – ( -2)

Solution:

1. (-5 )+ 9 = 4  [Subtract and put the sign of greater number]
2. (-1) – ( -2)

⇒ (-1) + (-2)   [Transform subtraction problems into addition problems]

⇒ (-1) + (2)    [Subtract and put the sign of greater number]

Hence,

(-1) – ( -2) = 1

Example 2: Add -10 and -19.

Solution: -10 and -19 are both negative numbers. So if we add them, we get the sum in negative, such as;

(-10)+(-19) = -10-19 = -29

Example 3: Subtract -10 and -19.

Solution: (-10) – (-19)

Here, the two minus symbol will become plus. So,

-10 + 19 = 19 -10 = 9

Example 4: Evaluate 9 – 10 +(-5) + 6

Solution: First open the brackets.

9 – 10 -5 + 6

Add the positive and negative integers separately.

= 9 + 6 – 10 -5

= 15 – 15

= 0

### Practice Problems

2. Subtract 20 from 10
3. Find the sum of 12 and 13
4. Find the difference between 40 and 30

## Frequently Asked Questions – FAQs

### What is the rule to add integers?

The rules to add integers are:
+ and + is Sum
– and – is Sum with ‘-’ sign
+ and – is difference with sign of highest value

### What is the rule for subtraction of integers?

The rules to subtract integers are given here with examples:
-2 – 3 = -5
2 – (-3) = 5
2 – 3 = -1
3 – 2 = 1

### Are the rules addition and subtraction are same as rules for multiplication of integers?

Rules for multiplication of integers are different from addition and subtraction rules.
Two like signs when multiplied, they result in positive sign
Two unlike signs when multiplied, results in negative sign.
2 x 3 = 6
-2 x -3 = 6
-2 x 3 = -6

### Give examples of addition of integers.

The examples of addition of integers are:
10 + 9 = 19
10 + (-9) = 1
-10 + 9 = -1
-10 + (-9) = -19

### When two negative integers are added together, then what is the sign of resulted value?

When two negative integers are added together, the result is the sum of the two integers with a negative sign. For example,
-8 + (-4) = -8 – 4 = -12

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