Subtracting 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 or a mix. The subtraction of integers is an arithmetic operation performed on integers with the same sign or with different signs to find the difference. Let us learn more about subtracting integers in this article.

There are certain rules to be followed to subtract two integers. Integers are complete numbers that do not have fractional parts. It includes positive integers, zero, and negative integers. The rules for subtracting integers are given below:

• If we subtract 0 from any integer, the answer will be the integer itself.
• If we subtract any integer from 0, we will find the additive inverse or the opposite of the integer.
• 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 of the absolute numbers and place the sign of the bigger number in the result.

The table given below shows the subtracting integer rules with examples.

Subtracting Integers with the Same Sign

When we subtract two integers with the same sign, we subtract their absolute values and place the common sign in the result. The absolute value of a number is the positive value of the given number. For an instance, the absolute value of 6 is 6, the absolute value of -6 is 6, etc. For subtraction of integers, we change the sign of the subtrahend. For example, -2 -(-5), can be written as -2 + 5. Now, the absolute value of 5 is 5, and of -2 is 2. By subtracting 2 from 5, we get 3. Since 5 > 2, the sign of the answer will be the same as the sign of 5, which is positive. Therefore, -2 -(-5) = 3.

Here, it is important to note that every subtraction fact can be written as an addition fact. For example, 4 - 7 is the same as 4 + (-7).

Some examples of subtracting integers with the same sign are given below:

• (-1) - (-6) = -1 + 6 = 5
• 3 - 8 = -5
• 24 - 17 = 7

Subtracting Integers with Different Signs

Subtracting two integers with different signs is done by changing the sign of the integer that is subtracted. Then, we need to check if both the integers become positive, the result will be positive and if both the integers are negative, then 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 with another method in which we add the absolute values, and then attach the sign of the minuend with 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 of 5 is 5. Now, find the sum of these absolute values which is 9 + 5 = 14. As 5 is the minuend here with a positive sign, so the answer sign will be positive. Therefore, 5 - (-9) = 14.

The subtraction of integers on a number line is based on the given principles:

• Every subtraction fact can be written as an addition fact.
• Adding a positive number will be done by moving towards the right side (or the positive side) of the number line.
• Adding a negative integer will be done by moving towards the left side (or the negative side) of the number line.
• Any one of the given integers can be taken as the base point from where we start moving on the number line.

Now, let us learn how to subtract integers on a number line. The first step is to choose a scale on the number line. For example, if we want to plot numbers in multiples of 1, 5, 10, 50, etc., depending on the given integers. For example, in subtracting 10 from -30 we can take a scale of 10 on the number line to ease our work. However, if we have to subtract -2 from 7, we can take a scale of counting numbers starting from 1. Then, we need to express the given subtraction expression into an addition fact by changing the sign of the subtrahend.

The next step is to locate any one of the integers on the number line, preferably a number with a greater absolute value. For example, if you need to subtract 4 from 29, it is better if we locate 29 on the line first and then take 4 jumps towards the left, rather than locating -4 and then taking 29 jumps.

The third and final step is to add the second integer to the number located in the previous step by taking jumps either to the left or to the right depending on whether the number is positive or negative.

Let us take an example to understand this better.

Example: Subtract -4 from -7

Solution: For subtracting integers on a number line let us follow the steps given below:

• Step 1: The expression can be written as -7 - (-4). Draw a number line with a scale of 1.
• Step 2: Express -7 - (-4) as an addition expression by changing the sign of the subtrahend from negative to positive. We get -7 + 4.
• Step 3: Start from -7, take 4 jumps to the right side as we are adding 4 to -7.

Therefore, -3 is the required answer.

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How to Subtract Integers?

Subtracting integers involves certain rules that need to be followed. The basic rules for subtracting integers are given below:

• If we subtract 0 from any integer, the answer will be the integer itself.
• If we subtract any integer from 0, we will find the additive inverse or the opposite of the integer.
• 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 of the absolute numbers and place the sign of the bigger number in the result.

What is the Rule for Subtracting Negative Integers?

If both integers are negative, then to subtract them, we will first write it as an addition fact. Then, we find the difference between their absolute values and attach the sign of the number with the greater absolute value with the result. For example, let us subtract -45 from -23. It can be written as -23 - (-45). We can re-write it as -23 + 45. Now, the difference between the absolute values is 45 - 23 = 22. Since 45 >23, the answer sign will be the same as the sign of 45 which is positive. Therefore, -23 - (-45) = 22.

What is a General Rule for Subtracting Integers?

The general rule for subtracting integers is given as follows:

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. For example, 1 - (-9) can be written as 1 + 9 after changing the sign of the subtrahend, which gives the result as 1 + 9 = 10. In another example, if after changing the sign of the subtrahend we get both the numbers with different signs, then we find the difference of the absolute values and write the sign of the bigger number. For example, in -4 - (-8), Here, we get -4 + 8, so after finding the difference of the absolute values we get 4 and the sign of the bigger number is positive, so we will write the answer as 4.

What is the Rule for Subtracting Integers with Different Signs?

For subtracting integers with different signs, we follow the steps given below. Let us subtract -5 from 6. This means 6 - (-5)

• Step 1: First, we will change the sign of the subtrahend which is -5. This makes it 5.
• Step 2: Find the sum of the new integers, that is 6 + 5 = 11.
• Step 3: The result is 11.

What is the Rule for Subtracting Integers with the Same Sign?

To subtract integers with the same sign, we first change the sign of the subtrahend. Then, find the difference between the absolute values of both the integers. Attach the sign of the number with the greater absolute value with the answer. For example, (-9) - (-3) = -9 + 3 = -6.

How is Subtracting Integers Related to Adding Integers?

Addition and subtraction are inverse operations. It means every addition expression can be expressed in subtraction and vice-versa. Subtracting integers is related to adding integers because both can be expressed in each other's form. For example, we can write 12 + (-9) as 12 - 9. Similarly, we can write - 23 - 5 as -23 + (-5).

What is the first Step in Subtracting Integers?

The first step in subtracting integers is to change the sign of the subtrahend. After this, the procedure of subtraction can be followed. For example, if we need to subtract 8 from 13, we can write it as, 13 - (+8). Now, we can change the sign of the subtrahend which is 8 and it becomes 13 - 8. Now, we can the difference of 13 and 8 which is 5 and the sign of the result will be the sign of the bigger number. In this case it is positive so 13 - 8 = 5

What is an Example of Subtracting Integers?

Some examples of the subtraction of integers are listed below:

• 13 - 8 = 5
• (-39) - (-14) = -25
• -16 - 4 = -20
• 2 - (-88) = 90