Additional and Subtraction: The Basics of Arithmetic

Posted on July 11, 2023

Editor Kangaroo Math

Mathematics may seem confusing and frustrating at times, but it wasn’t always that way.

Math began as a simple way to communicate ideas and describe our world.

That’s where arithmetic came in. It was the first kind of math developed by humans and it involved basic operations like addition and subtraction.

Addition: Combining Numbers

Addition is the most basic arithmetic operation. It’s about combining two numbers to get a single number, also called a sum.

Let’s look at an example: if you have two apples from one vendor and three from another, how many apples do you have in total?

You can count and see that you have five apples. Mathematically, we represent this with the symbols we commonly use today. We write 2 + 3 = 5.

This equation means “two plus three equals five.” The plus symbol means “and” and the equals sign means “is.” So, when we add two and three, we get the sum, which is five.

Subtraction: Finding the Difference

Subtraction is the opposite of addition. Instead of finding the sum, we find the difference between two numbers.

Let’s say you bring all five apples home and eat one of them. How many apples are left? You can count and see that there are four apples left. But we can also calculate this using subtraction.

We write 5 – 1 = 4. This equation means “five minus one equals four.” It tells us that when we subtract one from five, we get four.

Properties of Addition and Subtraction

Now that we understand addition and subtraction, let’s talk about some important properties of these operations:

Addition Properties

Addition is commutative: The order of the numbers being added doesn’t matter. For example, 2 + 3 is the same as 3 + 2. Both equal 5.5
Addition is associative: The grouping of numbers being added doesn’t matter. For example, (2 + 3) + 4 is the same as 2 + (3 + 4). Both equal 9.

Subtraction Properties

Subtraction is not commutative: The order of the numbers being subtracted does matter. For example, 3 – 2 is not the same as 2 – 3.
Subtraction is not associative: The grouping of numbers being subtracted does matter. For example, (5 – 3) – 2 is not the same as 5 – (3 – 2).

Understanding the Basics

It’s important to remember that even though math can get more complex, the symbols and operations are based on concrete concepts.

They represent real-world ideas and relationships. The goal of this series is to make all mathematical operations understandable and relatable, just like addition and subtraction.

By building a strong foundation in arithmetic, we can better grasp more advanced concepts. So let’s keep moving forward and learning more about math.

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