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Math for Kids23 chapters | 325 lessons

Instructor:
*Kelley Lipke*

Kelley has been teaching middle school for six years and has a master's degree in educational administration.

In this lesson you will learn about mathematical equations. You will find out what equations are composed of and how to solve them. There will also be a practice problem for you to try!

Max is planning a party for his friend and has been given $120 to spend on decorations. He has already spent $80 on balloons and wants to buy a box of streamers, also. If streamers cost $32 a box, will Max have enough money to buy them?

To determine if he has enough money for the streamers, Max needs to write and solve an equation.

An **equation** is a mathematical sentence that has two equal sides separated by an equal sign.

4 + 6 = 10 is an example of an equation. We can see on the left side of the equal sign, 4 + 6, and on the right hand side of the equal sign 10.

When solving math problems, like figuring out how much money Max has left to spend, a piece of the equation is going to be missing. The equation for Max's problem will look like this:

As you can see, equations can also have constants, coefficients, variables, and operators.

Constants are numbers that do not change. 80 is the constant in this example.

A coefficient is a number attached to a variable. Coefficients are used in multiplication equations. For example, 12 is the coefficient in the equation 12*n* = 24.

A variable is a letter that represents an unknown number. In this problem, *b* is the variable and is the part we need to solve for.

An operator tells you which operation to use and includes addition, subtraction, multiplication, and division.

To solve this equation, Max needs to get the variable on one side by itself. He does this by using inverse operations. **Inverse operations** are like opposites. Whatever operation we see in an equation, we use the inverse of that operation to solve. In this case, the operator is an addition sign. So, we will use the inverse operation, subtraction, to isolate the variable.

Also, because equations have an equal sign, they must always remain equal and balanced. In other words, whatever we do to one side of the equation, we need to do the same to the other side. Let's try it!

The first step in isolating the variable is to subtract 80 from both sides of our equation. The 80s on the left side undo or cancel each other. Now our variable, *b*, is by itself.

Since we subtracted 80 from one side of the equation, we must also do it on the other side:

Therefore, Max has $40 left. He can buy one box of streamers.

OK. Now, it is your turn. So, get a piece of paper and a pencil. I'm going to give you the problem but don't scroll down to see the solution until you've tried to solve it yourself.

Oscar is saving up to buy a bicycle that costs $245. If he already has $62 saved, how much more money does he need to buy the bike?

Here is our equation:

Think you're finished? OK. Keep reading to see if you've solved it correctly.

First, since the operator is a 'plus' sign, we know we need to do the inverse operation, subtraction, to isolate the variable.

Second, we also know that what we do on one side, we must do to the other.

So, by subtracting 62 from each side of the equation, we can see that *x* = 183.

Oscar needs to save $183 to have enough to buy the bike.

While you may identify an equation by its equal sign, **equations** may also consist of constants, variables, coefficients, and operators. When solving equations, it's important to use **inverse operations** on both sides of the equation, so you are always keeping it balanced.

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10 in chapter 10 of the course:

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Math for Kids23 chapters | 325 lessons

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