## Introduction to Algebra

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- Category: Algebra

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**INTRODUCTION TO ALGEBRA**

In this lesson we will begin to learn about Algebra. Algebra is a branch of Mathematics that substitutes letters for numbers. Algebra is about putting real life problems into equations and solving those equations using letters and symbols. In other words, we can say Algebra is the area of mathematics where letters, like x or y, or other symbols are used to represent unknown numbers.

If you want to do anything, like launch a spaceship into orbit, or make money in business, you will need Algebra. It is a tool that you can use to solve real world problems and there are very few jobs in science or business that won’t use Algebra.

The great news is that Algebra is fun and easy to learn if you just learn some basic rules. Remember that the more you practice, the easier it will become.

First, let’s learn a few basic terms that we will use while we are discussing Algebra.

The first term that we will learn is **constant**. A constant is a fixed quantity or value that does not change. We can simply say that constants are numbers. For example, the numbers 3, 5, -8 and 1/2 are all constants.

The second term that we will learn is** variable**.A variable in Algebra is defined as a symbol that can have different values. Think of variables as containers that can hold different values inside themselves. The values that they hold can change, or vary, and so we call them variables.

As mentioned, Algebra is all about solving real world problems. Whenever we want to solve a problem, we always follow some rules and steps. Let’s look at an example and learn the simple steps to solve any problem.

Imagine that we want to create a mathematical equation that shows my current age in relation to my father’s current age. If I tell you that my age is half of my father’s age, we can begin to create the mathematical expression.

The first step is to say what constants and variables are being used and what their values are. This is called declaring the constants and variables. We use the word “Let” to begin the declaration of each variable. For example, we would say “Let x equal my age” and “Let y equal my father’s age” We write this as:

Let y=my father’s age

Now that we have declared the variables, we will put them into an equation that looks like this: X equals Y divided by two.

x = y/2

We can read this expression as: my age equals my father’s age divided by two. If I tell you that my father is 50, we can use the expression we have just created to determine my age. We know from the declarations that my father’s age equals y, so we just substitute the value of y with 50, like this: x equals 50 divided by two

x=50/2

Now we solve the right hand side of the equation. 50 divided by 2 equals 25. This means that x equals 25.

Let’s look at another example of a simple problem we can solve using Algebra. Imagine I tell you that my friend caught 3 times as many fish as me and I want to turn that information into a mathematical expression.

Remember that the first step is to say what constants and variables are being used and what their values are. We call this declaring the constants and variables. Remember we use the word “Let” to begin the declaration of each variable.

For example, we would say “Let x equal how many fish I caught” and “Let y equal how many fish my friend caught”. We write this as:

Let x=fish I caught

Let y=fish my friend caught

Now that we have declared the variables, we will put them into an equation that looks like this: Y equals three times X

y=3*x

We can read this expression as: The number of fish my friend caught equals 3 times the number of fish I caught. If I tell you that I caught 2 fish, we can use the expression we have just created to determine how many fish my friend caught. We know from the declarations that the number of fish I caught equals x, so we just substitute the value of x with 3, like this: Y equals three times two

y=3*2

Now we solve the right hand side of the equation. 3 times 2 is 6. This means that y equals 6 and so we know that my friend caught 6 fish.

These are just a couple of simple examples of what we can solve using Algebra. In future lessons, you will see more interesting problems that we can solve and you will soon understand why learning Algebra is not just fun, but also incredibly useful.