What is an Equation in Math? - Definition & Examples

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  • 0:00 Background Definitions
  • 1:00 What Is an Equation?
  • 2:06 Examples
  • 3:46 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you'll get a refresher on number sentences. You will then learn what equations are and how they can be useful in finding out missing information.

Background Definitions

Let's say your goal is to complete three Study.com lessons per day for the next four days. To find the number of lessons you'll have completed after those four days, we'll of course need to add together all the lessons you complete. The addition will look like this:

3 + 3 + 3 + 3 = 12

Which we can rewrite as:

3 * 4 = 12

These are number sentences. A number sentence is a string of numbers, mathematical operations, and an equal sign that tell you a mathematical fact. Like a regular text sentence, it's a basic unit of information.

Here's another example of a number sentence:

(3 - 1) * 5 = 10

Again, we have a set of numbers and operations that gives a mathematical fact. If we subtract 1 from 3 and then multiply that difference by 5, we do indeed get 10.

What is an Equation?

What if we took away part of a number sentence? For example, let's say you know that you want to complete 12 lessons, and you know you have time to complete 3 per day. But you need to know how many days it'll take. So our number sentence now looks like this:

3 * ? = 12

All we've done is insert a question mark in the place of our unknown value. Now, there's nothing wrong with question marks, but in math, we normally use a variable, which is simply a letter that we use to stand in for an unknown value.

Since a variable is simply a placeholder, it doesn't matter what letter we use. For the sake of convention, however, you'll often see x used as a variable. If we do so here, then our number sentence looks like:

3 * x = 12

The letter x is the number of days you'll need to work. We now have an equation, which is a number sentence in which a variable takes the place of unknown information.

In other words, if you take out part of a number sentence and replace it with a variable, you've created an equation.


Let's look at a new scenario. You own a dog who had 11 puppies. You've decided you can afford to keep 2. How many would you need to give away?

Well, let's look at the number sentence we would normally create here. We're starting with 11, and we'll be subtracting an unknown number of puppies. That would leave us with the 2 puppies you can keep. So:

11 - ? = 2

Again, we'll put a variable in the place of our unknown value. Since we're dealing with puppies here, we'll use the variable p. (Remember, we can use any letter as a variable, although x is a very commonly used variable.)

11 - p = 2

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