How To Subtract Integers Using Rules And Number Line
In order to fully understand the subtraction of integers, you first need to know what subtraction is. Subtraction is defined as one quantity being taken from another, which means that the two numbers are being "subtracted." The bigger number is called the minuend and the smaller number is called the subtrahend. In this article, we are going to learn about how to subtract integers and will see some of the integers examples.
Subtraction of Digits
Subtraction of Integers Definition
Subtraction of integers is a mathematical operation which is arithmetic in nature, and it involves the subtraction of two numbers. The objective of subtraction of integers is to find out how much bigger one number is than another or vice versa. It can be accomplished by subtracting the first integer from the second or by adding the difference between the two integers to a third integer.
The method of finding the difference between two integers is known as subtracting integers. Depending on whether the numbers are positive, negative, or a mix, the value may increase or decrease. Integer subtraction is an arithmetic operation that finds the difference between integers with the same or different signs.
Integers Rules
There are sure principles to be followed to subtract two numbers. Subtraction using an integers rules chart helps in understanding the sign convention. The guidelines for subtracting numbers are given below with integers examples:
Subtraction Using Integers Rules Chart
Following are the rules for subtracting integers:
When we subtract 0 from any integer, the result is the integer itself.
We may discover the additive inverse or opposite of any integer by subtracting it from 0.
Integer subtraction is accomplished by changing the sign of the subtrahend. If both numbers have the same sign, we add their absolute values and append the common sign. If the absolute numbers have different signs, we find the difference and place the sign of the larger number in the result.
Subtracting Integers with the Same Sign
When we subtract two integers with the same sign, we subtract their absolute values and add the common sign. The absolute value of a number is the number's positive value. For example, the absolute value of 9 is 9, the absolute value of -9 is 9, and so on.
We modify the sign of the subtrahend when subtracting numbers. For example, -3-(-5) can be written as -3+5. The absolute value of 5 is 5, and -3 is now 3. We get 2 by subtracting 3 from 5. Because 5>3, the answer's sign will be the same as the sign of 5, which is positive. As a result, -3-(-5)=2.
Here, it is important to note that every subtraction fact can be written as an addition fact. For example, 2-4 is the same as 2+(-4).
More examples:
(-1) - (- 6) = - 1 + 6 = 5
3 - 8 = - 5
24 - 17 = 7
Subtracting Integers with Different Signs
When subtracting two integers with different signs, the sign of the subtracted integer is changed. Then, if both integers become positive, the outcome will be positive; if both integers become negative, the result will be negative. For example, if we want to subtract (-9) from 5, that is 5-(-9), we will change the sign of 9 and then add the integers, which means it will be 5+9=14. Therefore, 5-(-9)=14.
This can also be understood using another way in which the absolute values are added, and the sign of the minuend is attached to the result. For example, if we want to subtract (-9) from 5, first we find the absolute values of both. The absolute value of -9 is 9, and 5 is 5. Now, find the sum of these absolute values, which is 9+5=14. As 5 is the minuend with a positive sign, the answer sign will be positive. Therefore, 5-(-9)=14.
Solved Examples
Example 1: Subtract the given integers using the rules for subtracting integers.
Subtract $-56$ from $-90$
Ans: This question is based on subtracting two integers with the same sign. Here, if we write it in the form of an expression, we get $-90-(-56)$. 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, $-90-(-56) = -34$.
Example 2: By using subtracting integers rules, find out which number should be added to 43 to get $-20$ as the answer.
Ans: Let $x$ be the number that should be added to 43 to get $-20$. So, we can form an equation in terms of $x$.
$x + 43 = -20$
To find the missing value, we need to solve the equation.
$x + 43 = -20$
$x = -20-43$
$x = -63$
Therefore, $-63$ has to be added to 43 to get $-20$.
Practice Problems
Q1. Find the value of (-1030) - 79.
Ans: -1109
Q2. Find the value of (-1030) + (-38).
Ans: -1068
Q3. Find the value of (-459) - (-38).
Ans: -421
Summary
As far as we have learned about subtraction, i.e. subtraction is defined as one quantity being taken from another, which means that the two numbers are being "subtracted." Then we see how integers affect the subtraction due to a change in the sign. In the integer rule, we have learned that subtracting Integers with the same sign and subtracting Integers with different signs, both show different results. So in this way, we now have command over the subtraction of integers.
FAQs on Subtraction Of Integers Explained With Rules And Examples
1. What is subtraction of integers?
Subtraction of integers is the process of finding the difference between two integers, which can be positive or negative numbers. In integer arithmetic, subtraction means removing a value from another value.
- Integers include positive numbers, negative numbers, and zero.
- Example: 7 − 3 = 4
- Example with negatives: 5 − (−2) = 7
2. How do you subtract integers using the number line?
To subtract integers on a number line, start at the first number and move left or right depending on the second number. Subtraction means moving left for positive numbers and right for negative numbers.
- Start at the minuend (first number).
- Move left if subtracting a positive integer.
- Move right if subtracting a negative integer.
- Example: 4 − 6 = −2 (move 6 steps left from 4).
3. What is the rule for subtracting negative integers?
The rule for subtracting negative integers is to change subtraction into addition and reverse the sign of the second number. This is known as the add the opposite rule.
- a − (−b) = a + b
- Example: 6 − (−3) = 6 + 3 = 9
4. Why does subtracting a negative number become addition?
Subtracting a negative number becomes addition because subtracting a negative is the same as adding its opposite. In integer arithmetic, two negative signs together create a positive effect.
- Mathematically: a − (−b) = a + b
- Example: 3 − (−5) = 3 + 5 = 8
5. How do you subtract a positive and a negative integer?
To subtract a positive and a negative integer, keep the first number and add the opposite of the second number. Always convert subtraction into addition of the opposite.
- Example 1: 8 − 3 = 5
- Example 2: 8 − (−3) = 8 + 3 = 11
6. What is the formula for subtraction of integers?
The formula for subtraction of integers is a − b = a + (−b). This means subtracting a number is the same as adding its opposite.
- Replace subtraction with addition.
- Change the sign of the second integer.
- Solve using integer addition rules.
7. Can you give an example of subtracting integers step by step?
Yes, subtracting integers step by step involves converting subtraction into addition and simplifying. Example: Solve −4 − 7.
- Step 1: Rewrite as addition → −4 + (−7)
- Step 2: Add the integers → −11
8. What is the difference between subtracting integers and adding integers?
The difference is that subtraction of integers requires changing the operation to addition of the opposite, while addition keeps the signs as they are. In subtraction, you apply the rule a − b = a + (−b).
- Addition example: 5 + (−2) = 3
- Subtraction example: 5 − (−2) = 7
9. What are common mistakes when subtracting integers?
A common mistake when subtracting integers is forgetting to change the sign of the second number. Always apply the add the opposite rule correctly.
- Incorrect: 6 − (−4) = 2
- Correct: 6 − (−4) = 6 + 4 = 10
- Forgetting sign changes leads to wrong answers.
10. How is subtraction of integers used in real life?
Subtraction of integers is used in real life to represent changes in temperature, money, elevation, and gains or losses. It helps calculate differences involving positive and negative values.
- Temperature drop: 5°C − 8°C = −3°C
- Bank balance: $10 − $15 = −$5
- Elevation change below sea level.
