Subtraction represents the value that’s been removed from the present value. But, in the case of integers, subtraction leads to an increase or decrease in the value of the given number. Students can find explanations of the Subtraction of Integers Definitions, Step by Step Procedure to Subtract Integers, Important Rules of Subtracting Integers, in the coming modules. When we subtract a negative integer from a number, the value of the given number will increase and if we subtract a positive integer the value will decrease.
Also, Read: Properties of Subtracting Integers
What is meant by Subtracting Integers?
An integer is one type of number without fractional numbers. It can be either a positive number, a negative number, or zero. Integers are a special set of numbers, which is represented by the letter “Z”. Few examples of integers are -9, -20, 0, 16, 37, and so on. The important properties that integers possess are associative property, distributive property, and commutative property. When two integers are subtracted, the difference value will be obtained.
Rules for Subtracting Integers | How to Subtract Integers?
While subtracting any integer we have to follow some simple rules. First, we have to convert the given subtraction problem into an addition problem. It means we have to convert the subtraction sign into an addition sign.
To convert the subtraction sign into an addition sign we need to follow some steps. The steps are:
- Initially, take the first integer and change its operation from subtraction to addition.
- Take the second number and find its opposite sign.
- Finally, they proceed with the normal addition process.
Subtracting Integers Possibilities
The subtracting integers have three possibilities. They are:
- Subtraction between two positive numbers.
- Subtraction between two negative numbers.
- Subtraction in between a positive number and a negative number.
Subtracting Integers Examples
Problem 1:
Subtract the given two positive integers. The given values are 8 and 12.
Solution:
As given in the question, the values are 8, and 12.
First, we have to change the operation. It means subtraction becomes an addition.
Now, change the sign of the second integer.
So, the values will be,
8 – 12
8 + (-12) = – 4
Therefore, the positive integers subtracted value is -4.
Problem 2:
Subtract one positive integer and one negative integer. So the positive integer is 3 and the negative integer is -14.
Solution:
Given the values,
Now, we have to change the operation, which means subtraction becomes an addition. Next, change the sign of the second integer, it gives us,
3 – (-14) = 3 + (14)
= 17
Therefore, after subtraction, the final value is 17.
Problem 3:
Subtracting two negative integers. The integers are -11 and -5.
Solution:
The given values are -11 and -5.
Now, we have to find the value using subtraction. First, we have to change the operation, which means subtraction becomes an addition.
Next, change the sign of the second integer.
So, the integers are,
(-11) – (-5) = (-11) + (5)
= -6
Hence, after performing subtraction the value is -6.
Problem 4:
Subtract -21 – 7 and write the final value.
Solution:
Given the values are -21, -7
Now, we have to change the operation. It means subtraction becomes an addition. Next, change the sign of the second integer.
So, it will be (-21) – (-7) = (-21) + (7) = 28
Thus, the final value is 28.
Problem 5:
John borrowed Rs 800 from Sony. John also borrowed Rs 200 from Sanju. What is the total amount of debt?
Solution:
Given the data,
John borrowed from Sony = Rs 800
John also borrowed from Sanju = Rs 200
The amount Rs 800 debt can be represented by= -800
The amount Rs 200 debt can be represented by=-200
The total amount of debt is =-800-200=-800+-200= -1000
Therefore, the total amount of debt is Rs 1000.
FAQs on Subtracting Integers
1. Can you subtract two integers which are having different signs?
Yes, we will subtract two integers having different signs.
2. What is the result for the subtraction of (6) – (-6)?
On subtracting (6) – (-6) we will get the result 12.
3. What happens when you subtract a negative sign from a positive sign?
When you subtract a negative sign from a positive sign will turn into an additional problem.
4. What is the rule of subtracting integers?
The rules of subtracting integers are given here with examples:
-4 – 3 = – 7
4 – (-3) = 7
4 – 3 = 1
3 – 4 = -1