How to Write Equations & Formulas

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  • 0:04 What Are Equations & Formulas?
  • 0:56 Pieces of an Equation
  • 1:57 Formulas as Special Equations
  • 2:24 Equation & Formula Components
  • 3:20 Word Problem Equations
  • 4:29 Lesson Summary
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Lesson Transcript
Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

Writing equations and formulas correctly is generally the first step toward solving or using them, especially in word problems or real-life situations. In this lesson, we will explore the steps for writing equations and formulas.

What Are Equations & Formulas?

'We're never going to get there!'

'Yes we are, Tommy. Why don't you do the math? We're traveling at 70 miles per hour, and we're 155 miles away. How long will it take us to get there?'

'I don't know!'

'Well, what's the formula for time traveled, in terms of distance and rate of speed?'

'Oh, you mean the d = rt thing?'

'Right! Now, if you fill in the distance and rate of speed, you can write an equation to solve for how long it will take us to get there.'

'Forget it - wake me up when we get there!'

As we can see from this scenario, solving life's pressing problems is often a matter of finding the right ingredients, setting up the math, and solving.

  • An equation is math's way of saying that two things are equal to each other--that is, they have the same value, are worth the same amount

  • A formula is a special equation that expresses an important relationship between variables and numbers.

Pieces of an Equation

You can always tell an equation by its equal sign (=). Equations can have constants, which are values that are known, as well as variables, which are unknown values typically expressed with letters.

Here's some simple equation examples:

5 + 6 = 11

x + 4 = 15

Take a look at the simple equation you might see that assigns value to a variable:

x = 5

Equations don't have to have any numbers at all. For example, you might find that two variables are equal to each other. Any time you see an equal sign, you know you're looking at an equation. That is the difference between an equation and an expression, which is a mathematical relationship between variables and/or numbers but without setting the expression equal to something else, like this one:

5c + 2

We can change an expression into an equation by setting it equal to something, like this one:

x + 5 = 10

The question you are trying to answer here is what value plus 5 equals 10. The answer, of course, is 5.

Formulas as Special Equations

A formula has more than one variable and uses these multiple variables to express an important relationship. For example, d = rt is a formula for solving 'distance traveled' problems. Notice that when variables are stuck together with no operation sign between them, that means to multiply them. So, in the d = rt formula, rate of speed (r) and time traveled (t) are multiplied together to get the total distance traveled (d).

Equation & Formula Components

In algebra, equations and formulas are made up of terms , which are groups of variables and numbers that are connected by multiplication and division. The terms are then tied together by the equal sign and by addition and subtraction operations.

Generally, a term like -9xy may have the following:

  • A coefficient, which is a number that is being multiplied by the rest of the term
  • One or more variables, multiplied together
  • Exponents, which are the number of times that a variable is multiplied by itself

In 5x², the 5 is multiplied by the rest of the term. An exponent of 2 means that there are actually two x's, being multiplied together. This term means 5 times x times x.

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