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Big Ideas Math Common Core 8th Grade: Online Textbook Help10 chapters | 63 lessons

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.

'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!'

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.

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

Equation examples: 5 + 6 = 11; x + 4 = 15

Take a look at the image of a simple equation you might see that assigns value to a variable.

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.

We can change an expression into an equation by setting it equal to something.

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*).

In algebra, equations and formulas are made up of **terms** , 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 may have

- a
**coefficient**(a number that is being multiplied by the rest of the term); - one or more variables, multiplied together; and
**exponents**(number of times that a variable is multiplied by itself).

In 5*x*², 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*.

Each side of an equation or formula will have one or more terms, tied together by addition or subtraction. The two sides of the equation or formula will be equal (have the same value).

A **word problem** is a math problem presented in a story format, instead of a written equation. One of the steps in solving a word problem is writing the equation or formula that is appropriate for the situation. For example:

Mary had 5 pieces of candy on the table. Marcia came in and added some more. When Mary counted all of the pieces, there were a total of 11 pieces of candy on the table. How many pieces of candy had Marcia added to the 5 that Mary had on the table?

There's not really a formula like *d* = *rt* for this situation, but we can write an equation for it, fairly easily. Going through what we know from the problem, we can:

- Write a 5 for Mary's original pieces of candy. '5'
- Put a plus sign ('+') next to the 5, since Marcia came in and added some. '5 + '
- Place a variable on the other side of the '+' to represent the unknown amount of candy that Marcia added. '5 +
*x*' - Place an equal sign to show that there is a total amount of candy. '5 +
*x*= ' - Write in the total amount of the candy, given in the problem. '5 +
*x*= 11'

That's it! You've written the equation for the word problem!

An **equation** is a way to say that one thing is equal to, or the same value as another. A **formula** is a special equation that expresses an important relationship between variables expressing commonly-used ideas, like speed, temperature, etc. An **expression** is a relationship between values and/or variables that has no equal sign. **Variables** (placeholders for values we don't know) may be placed side by side in a formula or equation to show multiplication of those variables. A word problem may be translated into an equation or formula by assigning the correct symbol or number to each value, unknown, and relationship in the word problem, and writing it as a simple mathematical statement.

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Big Ideas Math Common Core 8th Grade: Online Textbook Help10 chapters | 63 lessons

- Solving Linear Equations: Practice Problems 5:49
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- How to Solve Equations with Multiple Steps 5:44
- Addition Property of Equality: Definition & Example 3:51
- Subtraction Property of Equality: Definition & Example 3:54
- Multiplication Property of Equality: Definition & Example 4:05
- Division Property of Equality: Definition & Example 3:51
- Distributive Property: Definition, Use & Examples 6:20
- How to Write Equations & Formulas
- Go to Big Ideas Math 8th Grade Chapter 1: Equations

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