Back To Course

ELM: CSU Math Study Guide16 chapters | 140 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.

We should always remember that algebra has a basis in real life. When we have all these variables and exponents and things, that's easy to forget. But the purpose of algebra is to help us find answers to real situations.

For example, let's say that you have a part-time job as a dog walker. You earn $15 each time you walk a dog. If *d* is the number of dogs you walk, your total income is $15*d*, or $15 times the number of dogs. That's an algebraic expression. And what if you had 6 walks scheduled this week? How much will you earn? That's where we get to evaluating algebraic expressions, our topic for this lesson.

**Evaluating algebraic expressions** is when you substitute a number for each variable and then solve the expression. These types of problems typically look like this: Evaluate 15*d* when *d* = 6.

So this is our dog walking scenario. And you can see there are two parts to the question. First, there's an algebraic expression. This is a mathematical sentence of sorts that contains one or more variables. Here, it's 15*d*. Second, there's a sample value for the variable. In this case, we have *d* = 6.

To solve this problem, we take the value and plug it into our expression. So we'd replace the *d* in 15*d* with a 6. We complete the problem by multiplying 15 times 6, which gets us 90. That's our answer! You'll earn $90 this week - plus you'll get lots of exercise, which is kind of its own payment, right? Well, okay, the money's good, too.

Evaluating algebraic expressions can be pretty straightforward. Whether you have one variable or ten, it's really just plugging them in and solving. Usually, the trickiest part is remembering the order of operations. The **order of operations** is a system that determines which procedures occur first in an expression.

As you'll recall, the mnemonic **PEMDAS** gives us our order. PEMDAS stands for *parentheses, exponents, multiplication, division, addition and subtraction*. You might remember PEMDAS with the phrase *Please Excuse My Dear Aunt Sally*. This mnemonic makes inoffensive Aunt Sallys everywhere cringe. Offensive Aunt Sallys don't care what you say about them.

But why do we care about Aunt Sally? Well, if we had 4 - 2 * 3, would we do 4 - 2, which gets us 2, then multiply that by 3, which gets us 6? Or would we multiply 2 * 3, which gets us 6, then subtract that from 4, which gets us -2? Those are two totally different answers. PEMDAS tells us multiplication precedes subtraction, so -2 is the correct answer.

Also, remember that multiplication and division are linked, as are addition and subtraction. Or, 'my dear' is a package deal, as is 'Aunt Sally.'

Ready to try some practice problems? Almost. First, a warning. It's critical that you always use parentheses. Did you ever go on a carnival ride where they tell you to keep your arms inside the ride? Parentheses are the ride, and minus signs are the numbers' arms. They even kind of look like arms, which is a bonus.

Here's why this matters. Let's say you have *x*2 - 3 and you want to evaluate it when *x* = 2. Okay, no problem. That's 22 - 3. Exponents are first, so I square the 2 and now I have 4 - 3. That's easy: 1. You might be thinking, 'I don't need parentheses. I solved that problem without them just fine.'

Okay, what if *x* = -2? So we have -22 - 3. Again, I square the 2 and I get -4 - 3. That will be -7. And that's wrong. You should have squared not just 2 but -2. Then you'd get 4 - 3 and again get 1.

That would've been easy to remember if you'd written the expression as (-2)2 - 3. So consider this a safety reminder: Always use parentheses. Don't let your numbers lose their arms.

Okay, let's practice evaluating some algebraic expressions. Let's start simple: Evaluate *y* - 2 when *y* = 10. Just plug 10 in for *y*: 10 - 2. Then solve. Our answer is 8. That means that when *y* = 10, *y* - 2 equals 8.

Here's another: Evaluate *a*2 + 5 when *a* = 3. If we plug 3 in, we get 32 + 5. Now, remember PEMDAS. Exponents come before addition. So we first square the 3 to get 9 + 5. And 9 + 5 is 14. So when *a* = 3, *a*2 + 5 = 14.

Let's get more complicated: Evaluate 4*xy*3 - 12 when *x* = -2 and *y* = 3. Okay, don't worry. We can handle this. The first step is to plug in our *x* and *y* values. We get 4(-2)(3)3 - 12. Never forget those parentheses. Keep your arms and minus signs inside the ride.

Now, it's 'please excuse my dear Aunt Sally' time. We'll start with the exponent. 33 is what? 3 * 3 = 9 and 9 * 3 = 27. So now we have 4(-2)(27) - 12. The next step is multiplication. 4 * (-2) = -8. And -8 * 27 = -216. That gives us -216 - 12. That's -228. That's our answer!

I think you can handle one that's even harder: Evaluate:

when *a* = 4 and *b* = -2. Okay, that's a big messy one. But just follow these steps. First plug in our *a* and *b* values. We get:

And what about Aunt Sally? Okay, parentheses are first, so let's tackle that stuff inside the parentheses. 42 is 16 and -23 is... 8 or -8? It's -8. So we have 16 + (-8), which is 16 - 8, or 8.

Let's look at where we're at.

Let's simplify that to 16/(-8). And that'll just be -2. That big messy problem? It's just -2. Not bad! Always remember, if you can please excuse my dear Aunt Sally, you can evaluate algebraic expressions.

In summary, evaluating algebraic expressions is when you substitute a number for each variable and then solve the expression. Usually, the trickiest part is remembering the order of operations. For this, we use PEMDAS. This stands for *parentheses, exponents, multiplication, division, addition and subtraction*. You can remember the acronym with the phrase *Please Excuse My Dear Aunt Sally*.

When this lesson is done, you should be able to confidently evaluate simple algebraic expressions using the order of operations.

To unlock this lesson you must be a Study.com Member.

Create your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
3 in chapter 6 of the course:

Back To Course

ELM: CSU Math Study Guide16 chapters | 140 lessons

- What is a Variable in Algebra? 5:26
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- The Distributive Property and Algebraic Expressions 5:04
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Go to ELM Test - Algebra: Basic Expressions

- Data Science for Marketing
- Individual Creativity in the Workplace
- Leadership in Action for Coaches
- Introduction to the Internet of Things
- Adaptive Leadership for Agile Organizations
- Logical vs. Creative Thinking in the Workplace
- Adaptive Technology & Innovation
- Marketing Analytics
- World Music Overview
- Big Data Analytics & Application
- Average AFQT Scores
- ASVAB Test Day Preparation
- How To Pass the GED Reading Test
- What is the AFQT?
- What is the Highest ASVAB Score?
- ASVAB Scores for Marines
- Can You Retake the ASVAB?

- History of Photography Materials & Techniques
- Basketry: Materials, Techniques & Processes
- Surface Area of a Pentagonal Prism
- Displaying Three-Dimensional Art: Methods & Techniques
- The Role of the Trauma Nurse in Injury Prevention & Outreach
- Common Practice Style & Developing Tonal Harmony
- Flast v. Cohen: Case Brief, Decision & Dissent
- Leadership with Intention & Reflection
- Quiz & Worksheet - Native American Art History
- Quiz & Worksheet - Mrs. Van Daan in Diary of a Young Girl
- Quiz & Worksheet - Fiber Art Materials Terms
- Quiz & Worksheet - Inheritance in Java
- Quiz & Worksheet - Processes in Sculpting
- Introduction to Research Methods in Psychology Flashcards
- Clinical Assessment in Psychology Flashcards

- Gerontology for Teachers: Professional Development
- The Civil War & Reconstruction for Teachers: Professional Development
- Astronomy 101 Syllabus Resource & Lesson Plans
- TCI History Alive World Connections: Online Textbook Help
- Pathophysiology for Teachers: Professional Development
- How to Measure Perimeter, Area & Volume
- Campbell Biology Chapter 13: Meiosis and Sexual Life Cycles
- Quiz & Worksheet - Characteristics of Neurological Conditions
- Quiz & Worksheet - Evidence for the Big Bang Theory
- Quiz & Worksheet - Simple & Complex Carbohydrates in the Diet
- Quiz & Worksheet - Demographics & Health
- Quiz & Worksheet - Definition & Function of IGD

- Lady Macbeth: Quotes & Character Analysis
- What is Psychosis? - Symptoms & Definition
- Day of the Dead Lesson Plan
- Homeschooling in Montana
- SBEC Technology Application Standards for Teachers
- Next Generation Science Standards for Middle School
- Books for Guided Reading
- Response to Intervention (RTI) in Ohio
- Reading Games for Kids
- Wisconsin Science Standards
- Utah Science Standards for 4th Grade
- WIDA Can Do Descriptors for Grade 2

Browse by subject