Subtraction of Integers: Properties, Rules with Solved Examples

Subtraction is one of the basic operations of arithmetic, along with addition, multiplication, and division. It is the operation of finding the difference between two numbers. The sign of the answer to a subtraction problem tells us whether the first number is greater than, less than, or equal to the second number. In this blog post, we will explore the properties and rules of subtracting integers with solved examples.

Properties of Subtraction of Integers

Subtraction is one of the basic operations of arithmetic, with the other being addition. Subtraction of integers is a little bit different than subtracting whole numbers, but the same principles apply. In this section, we’ll review the properties of subtraction and some rules to help make subtracting integers a little easier.

One important property of subtraction is that it is not commutative, which means that the order of the operands matters. For example, 5 – 3 is not the same as 3 – 5. This can be a little tricky when subtracting negative numbers, so it’s important to keep this in mind.

Another property of subtraction is that it is associative, which means that you can change the order of the operation without changing the result. For example, (5 – 3) – 2 is equal to 5 – (3 – 2), which is equal to 5 – 1 or 4.

When subtracting integers, you can think of it as “moving” along a number line in either direction. If you’re subtracting a positive number, you’re moving left on the number line; if you’re subtracting a negative number, you’re moving right on the number line. For example, if we start at 0 on a number line and move 5 units to the right, we’ll end up at 5. But if we start at 0 and move 3 units to the left first, then move 2 more units to the

Introduction to Integers

Integers are the foundation of arithmetic and are defined as the set of whole numbers and their opposites. Every number on the number line is an integer. The basic rules for subtracting integers are to subtract the numbers as if they were positive and then to add the sign of the smaller number. These rules can be applied to any two integers regardless of their size or sign.

When subtracting a larger number from a smaller number, the answer will always be negative. For example, when subtracting 7 from 3, the answer will be -4 because 3 is less than 7. This rule applies regardless of whether the numbers are positive or negative.

Another rule to remember when subtracting integers is that the sign of the answer will be determined by the sign of the integer with the larger absolute value. Absolute value is simply the distance from zero on the number line without regard for direction. For example, 8 has a larger absolute value than 6 because it is further away from zero on the number line, even though 6 is a higher number. Therefore, when subtracting 8 from 6, the answer will be -2 because 8 has a larger absolute value than 6.

Here are some examples of subtracting integers:

5 – 3 = 2
-6 – (-4) = -2
-7 – 3 = -10

Basic Terminology Related to Integers

Subtraction is one of the four basic operations of arithmetic, with the other three being addition, multiplication and division. Subtraction can be thought of as the opposite of addition. In other words, subtraction is the process of finding the difference between two numbers.

When subtracting integers, there are a few properties and rules that you need to be aware of. These are:

The Commutative Property: This states that the order in which two numbers are added or subtracted does not matter. For example, 5 – 3 = 2 and 3 – 5 = -2.

The Associative Property: This states that when adding or subtracting more than two numbers, the order in which they are added or subtracted does not matter. For example, (5 – 3) – 4 = -2 and 5 – (3 – 4) = 6.

The Identity Property: This states that when 0 is added to any number, or when any number is subtracted from itself, the result is always the original number. For example, 5 + 0 = 5 and 5 – 5 = 0.

The Additive Inverse Property: This states that for any integer a, there exists an integer b such that a + b = 0. In other words, every number has an opposite number. For example, if we take 3 then its opposite would be -3 because 3 + (-3) = 0. Similarly, if we take –

Properties of Integers

Integers are whole numbers that can be positive, negative, or zero. The properties of integers are some of the rules that apply to them.

Here are the properties of integers:

1. Integers are closed under addition and subtraction. This means that when you add or subtract two integers, the result is always an integer.

2. Integers are commutative under addition and subtraction. This means that the order of the integers does not affect the result. For example, 3 + 5 = 5 + 3 = 8.

3. Integers are associative under addition and subtraction. This means that you can group the integers in any way you want and the result will still be the same. For example, (3 + 5) + 7 = 3 + (5 + 7) = 15.

4. Every integer has an additive inverse. This means that for every integer there is another integer that when added to it will give a sum of zero. For example, the additive inverse of 3 is -3 because 3 + (-3) = 0

Rules for Subtraction of Integers

When subtracting integers, there are a few rules to keep in mind:

1. The sign of the answer will be the same as the sign of the integer with the larger absolute value.

For example, if we’re subtracting a negative integer from a positive integer, the answer will be positive.

2.To find the answer, start by subtracting the smaller absolute value from the larger absolute value.

For example, to subtract -5 from 3, we would first subtract 3-5 to get -2. Then, because the answer has a negative sign, we would put a negative sign in front of it to get the final answer of -2.

3. If you’re subtracting two negative integers, add their absolute values together and put a negative sign in front of the answer.

For example, to subtract -5 from -3, we would first add 3+5 to get 8. Then, because both numbers were originally negative, we would put a negative sign in front of the answer to get -8.

Subtracting Integers with the Same Sign

When subtracting integers with the same sign, the rule is simple: just subtract the numbers as if they were regular whole numbers. The answer will have the same sign as the numbers being subtracted.

For example, let’s say we want to subtract -8 from -5. We would do this by subtracting 8 from 5, and because both numbers are negative, the answer will also be negative:

-5 – (-8) = -5 + 8 = 3

So, in general, if you’re subtracting two integers with the same sign, you can just ignore the signs and subtract the numbers as if they were positive. The answer will have the same sign as the numbers being subtracted.

Subtracting Integers with Different Signs

Subtracting integers with different signs can be a bit tricky. Here are the rules to follow:

If the signs are different, subtract the absolute value of the integer with the smaller absolute value from the integer with the larger absolute value. Then, take the sign of the integer with the larger absolute value.

For example, let’s say we want to subtract -6 from 3. We would first find the absolute value of each integer: -6 becomes 6 and 3 becomes 3. Then, we would subtract 6-3 to get 9. Since 3 has a larger absolute value than -6, we would take the sign of 3, which is positive. Therefore, our answer would be 9.

Subtracting Integers on a Number Line

When subtracting integers that are next to each other on a number line, the first integer is always the minuend and the second integer is always the subtrahend. The difference between the two integers is always the distance between them on the number line. To find this distance, count the total number of units from the minuend to the subtrahend. This will be the absolute value of the difference between the two integers. If the minuend is greater than or equal to the subtrahend, then the difference will be positive. If the minuend is less than the subtrahend, then the difference will be negative.

Conclusion

In conclusion, we have looked at the properties of subtraction of integers and some rules to follow when subtracting integers. We have also seen some solved examples to help understand these concepts better.

subtraction of integers is a vital mathematical operation that is used in many everyday situations. It is important to understand the properties and rules associated with this operation in order to be able to solve problems correctly.

Frequently Asked Questions

Q: What is the rule for subtracting integers?

A: The rule for subtracting integers is to change the sign of the second integer and then add the two numbers.