Subtracting Integers

Subtracting Integers

To find the Subtracting Integers, you have to subtract them. It could make the value go up or down, depending on whether the integers are positive, negative, or a mix of the two. To find the difference between two integers, you can subtract them if they have the same sign or if they have different signs. Let’s read this article to find out more about how to subtract whole numbers.

Subtracting Integers Rules

To find the difference between two whole numbers, you have to follow some rules. Integers are whole numbers that don’t have any parts that are fractions. It has both positive and negative integers, as well as zero. Here are the rules for Subtracting from whole numbers:

• If we Subtract 0 from any whole number, the answer is the number itself.
• If we take any integer and subtract it from 0, we get its additive inverse or the opposite.
• When subtracting integers, you change the sign of the number you’re taking away. After this step, if both numbers have the same sign, the absolute values are added together and the common sign is attached. If both numbers have different signs, we find the difference between the absolute numbers and put the sign of the larger number in the result.

Integers can be subtracted from each other by following the rules in the table below.

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

1. Subtraction between two positive numbers
2. Subtraction between two negative numbers
3. Subtraction between a positive number and a negative number

For ease of calculation, we need to renovate subtraction problems the addition problems. There are two steps to perform this which are given below.

Convert the subtraction sign into an addition sign.

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, finding the value of (-5) – (7)

Step 1: Change the subtraction sign into an addition sign

⇒ (-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]

Subtracting Integers with the Same Sign

When we subtract two integers with the same sign, we take their absolute values and put the same sign in the result. The positive value of a given number is its absolute value. The absolute value of 6 is 6, the absolute value of -6 is also 6, and so on. When subtracting two whole numbers, we change the sign of the number we’re taking away. For example, you can write -2 -(-5) as -2 + 5. Now, 5 has an absolute value of 5, and -2 has a value of 2. When we take 2 away from 5, we get 3. Since 5 is greater than 2, the answer will have the same sign as 5, which is a plus. So, -2 – (-5) equals 3.

It’s important to remember that every fact about subtraction can also be written as a fact about addition. For instance, 4 minus 7 is the same as 4 plus 7. (-7).

Here are some examples of how to subtract integers with the same sign:

(-1) – (-6) = -1 + 6 = 5

3 – 8 = -5

24 – 17 = 7

Subtracting Integers with Different Signs

When you want to subtract two integers that have different signs, you change the sign of the integer that you want to subtract. Then we need to check to see if the result is positive or negative. If both integers are positive, the result is positive, and if both are negative, the result is negative. For example, if we want to subtract -9 from 5, which is 5 – (-9), we will change the sign of 9 and then add the integers, so 5 + 9 = 14. So, 5 – (-9) equals 14.

You can also figure this out by adding the absolute values and then attaching the sign of the minuend to the result. If we want to take away -9 from 5, we first find the absolute values of both numbers. The value of -9 is 9, and the value of 5 is 5. Find the sum of these absolute values, which is 9 + 5 = 14. Since 5 is the minuend and has a plus sign, the answer sign will also be a plus. So, 5 – (-9) equals 14.

Subtracting Integers on a Number Line

On a number line, subtracting whole numbers is based on the following rules:

• Every fact about taking away can also be written as a fact about adding.
• When you add a positive number, you move toward the right side of the number line, which is also called the “positive side.”
• When you add a negative number, you move toward the left side of the number line, which is also called the negative side.
• Any of the given whole numbers can be used as the starting point for moving along the number line.

1. Now, let’s learn how to use a number line to subtract whole numbers. Choose a scale on the number line. This is the first step. For example, if we want to plot numbers that are multiples of 1, 5, 10, 50, etc., based on the integers we are given. For example, to make it easier to subtract 10 from -30, we can use a scale of 10 on the number line. But if we have to take away -2 from 7, we can use a scale of numbers that starts at 1. Then, we need to change the sign of the subtrahend to turn the given subtraction fact into an addition fact.
2. The next step is to find any integer on the number line, preferably one with a higher absolute value. For example, if you need to take 4 away from 29, it is easier to find 29 on the line and then jump 4 spaces to the left than to find -4 and then jump 29 spaces.
3. In the third and final step, you add the second integer to the number you found in the previous step. Depending on whether the number is positive or negative, you jump to the left or right.

Let’s look at an example to see how this works.

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.

Properties Of Subtraction Of Integers

• Closure property: The difference between any two given integers results in an integer.

For instance, 13 – 17 = – 4 and – 4 is an integer. In the same way, – 5 – 8 = – 13 and – 13 is an integer.

• Commutative property: The difference between any two given integers changes when the order is reversed.

For example, 6 – 3 = 3 but 3 – 6 = – 3.

So, 6 – 3 ≠ 3 – 6

• Associative property: In the method of subtraction, there is a change in the result if the grouping of 3 or more integers changes.

For example, (80 – 30) – 60 = – 10 however [80 – (30 – 60)] = 110.

So, (80 – 30) – 60 ≠ [80 – (30 – 60)].

Examples of Subtracting Integers : 

Example 1: Subtract the given integers by using the rules for subtracting integers.

Subtract:  -56 from -90

Solution: 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 : Subtract -19 from -10.

Solution: (-10) – (-19)

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

-10 + 19 = 19 -10 = 9

Example 3 : Subtract -7 from -12 using the rules of subtracting integers.

Solution: This question is based on subtracting integers with the same sign. Here, we have to subtract two integers with the same sign, -12 and -7.

-12 – (-7) = -12 + 7

= -5

Therefore, the difference between -12 and -7 is -5.

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