I still don't understand the challenge problems e⋅e−5ee, dot, e, minus, 5, e when e=5e=5e, equals, 5.What does this mean?

so, e(dot)e - 5e, the dot symbol represents multiplication. And 5e is another way to represent multiplication so, the expression actually looks like this: 5x5 - 5x5 which equals to 0 because 5x5 = 25, and 5x5 = 25, and subtracting 25 with 25 = 0. e(dot)e - 5e 5x5 - 5x5 = 25 - 25 25 - 25 = 0

If 9-8/x = ? and x=4 what do I do with the 8/x? Do I multiply add divide or subtract?

you substitute for x, so 9 - 8/4, do divide (8/4) first then subtract from 9.

If you don't know what y is, then you won't get an exact answer

Well you don't need to know what y is to solve the question. For example you have:6t=48. (if something is written like 6t, that always means you have to multiply, or any variable). So we have: 6t=48, we can divide both sides by 6 (we are dividing because you always do the inverse of what you are trying to solve, the opposite of multiplication is division) we have to divide both sides by 6 6t=48, 6/6 cancels out, 48/6=8. So now the equation would look like this: t=8, and now we know what t is we can verify it. 6t=48 or 6x8=48. And that's the beauty of Algebra! If you need more help just tell me. -Intellectual Genius

is it just me or is it way easier here than in class?

waaaaaaaaaaaaaay more easier than class. I think they make it dificult on purpouse so they look smarter!

i can't understand the question nine please help me understand

Start out with the variable. What is d worth? What do you need to do with that variable in the sentence? You should see that d is worth 4, and we need to now add that in the sentence. The sentence should now look like this - 8/4 + 3 Now, solve it like you would usually do it. 8/4 is equal to 2 (We need to do it first since it is the second in the Order of Operations), and then add 3 to that 2. You should get an answer of 5 if you did all that calculation correctly. Hope this helped!

what is it asking me when it says Evaluate 2y2y when y = 6y=6

It means you use substitution... You replace the "y" in "2y" with the value you are given. Since you were told to use "y=6", you take out "y" and replace it with 6. Remember, "2y" means "2 times y", so you need a multiplication symbol. Thus, "2y" becomes "2(6)". Then, you simplify the expression by doing the multiplication. Your final answer would be 12. Hope this helps.

How do you do this with fractions? (I'm really bad with fractions and math)

The process is no different. You replace each variable with its given value. Then you simplify the expression following order of operations rules and the rules for working with fractions. If you aren't great at working with fractions, then do yourself a favor and get more practice on that topic.

Why do we have to do multiplication and division first? Why to use these "order of operation"?

Here is why; "Because exponents are simply repeated multiplication, they are performed before multiplication. ... Thus the order: parentheses first, exponents second, mutiplication and division third, and save the lowest level operations of addition and subtraction for last." Personally I believe order of operation is way to balance the equation as well. :)

Does this topic have viable application to non-Algebra subjects, if any? Thanx.

Absolutely! There are many formulas that get used in real life situations. This teaches you how to use a formula and calculate a result based upon replacing values into the formula.

Main content

Evaluating expressions with one variable

Google Classroom

A mixture of explanations, examples, and practice problems to have you evaluating expressions with one variable in no time!

How to evaluate an expression with one variable

Let's say we want to evaluate the expression

a + 4

. Well, first we need to know the value of the variable

a

. For example, to evaluate the expression when

a = 1

, we just replace

a

with

1

\begin{aligned} a + 4 \\ = & 1 + 4 Replace a with 1 . \\ = & 5 \end{aligned}

So, the expression

a + 4

equals

5

when

a = 1

We can just as easily evaluate

a + 4

when

a = 5

\begin{aligned} a + 4 \\ = & 5 + 4 Replace a with 5 . \\ = & 9 \end{aligned}

So, the expression

a + 4

equals

9

when

a = 5

Evaluating an expression with multiplication

You might be asked to "Evaluate $3 x$ ‍ when $x = 5$ ‍."

Notice how the number

3

is right next to the variable

x

in the expression

3 x

. This means "

3

times

x

". The reason we do this is because the old way of showing multiplication with the symbol

\times

looks confusingly similar to the variable

x

Okay, so now let's solve the problem:

\begin{aligned} 3 x \\ = & 3 \cdot 5 Replace x with 5 . \\ = & 15 \end{aligned}

So, the expression

3 x

equals

15

when

x = 5

New ways to show multiplication

Hold on a second! Did you notice that we wrote "

3

times

5

" as

3 \cdot 5

instead of as

3 \times 5

? Using a dot instead of the symbol

\times

is another new way of showing multiplication:

3 \cdot 5 = 15

Parentheses can also be used to show multiplication:

3 (5) = 15

Let's summarize the new ways of showing multiplication that we learned.

	Old way	New way
With a variable	$3 \times x$ ‍	$3 x$ ‍
Without variable	$3 \times 5$ ‍	$3 \cdot 5$ ‍ or $3 (5)$ ‍

Evaluating expressions where order of operations matter

For more complex expressions, we'll have to be sure to pay close attention to order of operations. Let's take a look at an example:

Evaluate $5 + 3 e$ ‍ when $e = 4$ ‍.

\begin{aligned} 5 + 3 e \\ = & 5 + 3 \cdot 4 Replace e with 4 . \\ = & 5 + 12 Multiply first (order of operations) \\ = & 17 \end{aligned}

So, the expression

5 + 3 e

equals

17

when

e = 4

Notice how we had to be careful to think about order of operations when evaluating. A common wrong answer is

32

, which comes from first adding

5

and

3

to get

8

then multiplying

8

4

to get

32

Let's practice!

Problem 1

Evaluate the expression $9 - z$ ‍ when $z = 4$ ‍.

Challenge problems

Challenge problem 1

Evaluate $e \cdot e - 5 e$ ‍ when $e = 5$ ‍.

Want to join the conversation?

Sort by:

Joy
Posted 4 years ago. Direct link to Joy's post “I still don't understand ...”
I still don't understand the challenge problems e⋅e−5ee, dot, e, minus, 5, e when e=5e=5e, equals, 5.What does this mean?
Button navigates to signup pageComment on Joy's post “I still don't understand ...”
(55 votes)
Answer
- Littleman0562
  Posted 4 years ago. Direct link to Littleman0562's post “so, e(dot)e - 5e, the dot...”
  so, e(dot)e - 5e, the dot symbol represents multiplication. And 5e is another way to represent multiplication so, the expression actually looks like this: 5x5 - 5x5 which equals to 0 because 5x5 = 25, and 5x5 = 25, and subtracting 25 with 25 = 0.
  
  e(dot)e - 5e
  5x5 - 5x5 = 25 - 25
  25 - 25 = 0
  Comment on Littleman0562's post “so, e(dot)e - 5e, the dot...”
  (109 votes)
Morgan, Aaron
Posted 5 years ago. Direct link to Morgan, Aaron's post “If 9-8/x = ? and x=4 what...”
If 9-8/x = ? and x=4 what do I do with the 8/x? Do I multiply add divide or subtract?
Button navigates to signup pageComment on Morgan, Aaron's post “If 9-8/x = ? and x=4 what...”
(32 votes)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “you substitute for x, so ...”
  you substitute for x, so 9 - 8/4, do divide (8/4) first then subtract from 9.
  Comment on David Severin's post “you substitute for x, so ...”
  (44 votes)
Smith Dalton
Posted 6 years ago. Direct link to Smith Dalton's post “Why do we have to do mult...”
Why do we have to do multiplication and division first? Why to use these "order of operation"?
Button navigates to signup pageComment on Smith Dalton's post “Why do we have to do mult...”
(9 votes)
Answer
- moralisaiah
  Posted 5 years ago. Direct link to moralisaiah's post “Here is why; "Because exp...”
  Here is why; "Because exponents are simply repeated multiplication, they are performed before multiplication. ... Thus the order: parentheses first, exponents second, mutiplication and division third, and save the lowest level operations of addition and subtraction for last." Personally I believe order of operation is way to balance the equation as well. :)
  Comment on moralisaiah's post “Here is why; "Because exp...”
  (29 votes)
kme
Posted 4 years ago. Direct link to kme's post “If you don't know what y ...”
If you don't know what y is, then you won't get an exact answer
Button navigates to signup pageComment on kme's post “If you don't know what y ...”
(17 votes)
Answer
- Intellectual Genius
  Posted 4 years ago. Direct link to Intellectual Genius's post “Well you don't need to kn...”
  Well you don't need to know what y is to solve the question. For example you have:6t=48. (if something is written like 6t, that always means you have to multiply, or any variable). So we have: 6t=48, we can divide both sides by 6 (we are dividing because you always do the inverse of what you are trying to solve, the opposite of multiplication is division)
  
  we have to divide both sides by 6
  
  6t=48, 6/6 cancels out, 48/6=8. So now the equation would look like this: t=8, and now we know what t is we can verify it. 6t=48 or 6x8=48.
  
  And that's the beauty of Algebra!
  
  If you need more help just tell me.
  -Intellectual Genius
  Comment on Intellectual Genius's post “Well you don't need to kn...”
  (30 votes)
jonathan.christen
Posted 5 years ago. Direct link to jonathan.christen's post “what is it asking me when...”
what is it asking me when it says Evaluate 2y2y when y = 6y=6
Button navigates to signup pageComment on jonathan.christen's post “what is it asking me when...”
(14 votes)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “It means you use substitu...”
  It means you use substitution... You replace the "y" in "2y" with the value you are given. Since you were told to use "y=6", you take out "y" and replace it with 6. Remember, "2y" means "2 times y", so you need a multiplication symbol. Thus, "2y" becomes "2(6)".
  Then, you simplify the expression by doing the multiplication. Your final answer would be 12.
  
  Hope this helps.
  Comment on Kim Seidel's post “It means you use substitu...”
  (21 votes)
DJ
Posted 3 months ago. Direct link to DJ's post “why is this so easy?”
why is this so easy?
Button navigates to signup pageComment on DJ's post “why is this so easy?”
(18 votes)
Answer
- Liz
  Posted 3 months ago. Direct link to Liz's post “thats exactly how i feel”
  thats exactly how i feel
  Button navigates to signup page
  (13 votes)
ajlaanzayan
Posted 3 years ago. Direct link to ajlaanzayan's post “i can't understand the qu...”
i can't understand the question nine please help me understand
Button navigates to signup pageComment on ajlaanzayan's post “i can't understand the qu...”
(15 votes)
Answer
- pompano [hurt lol]
  Posted 3 years ago. Direct link to pompano [hurt lol]'s post “Start out with the variab...”
  Start out with the variable. What is d worth? What do you need to do with that variable in the sentence? You should see that d is worth 4, and we need to now add that in the sentence.
  
  The sentence should now look like this -
  8/4 + 3
  
  Now, solve it like you would usually do it. 8/4 is equal to 2 (We need to do it first since it is the second in the Order of Operations), and then add 3 to that 2. You should get an answer of 5 if you did all that calculation correctly.
  
  Hope this helped!
  Comment on pompano [hurt lol]'s post “Start out with the variab...”
  (13 votes)
Mateo Gonzalez
Posted 3 months ago. Direct link to Mateo Gonzalez's post “is it just me or is it wa...”
is it just me or is it way easier here than in class?
Button navigates to signup pageComment on Mateo Gonzalez's post “is it just me or is it wa...”
(17 votes)
Answer
- PADAWAN
  Posted 2 months ago. Direct link to PADAWAN's post “waaaaaaaaaaaaaay more eas...”
  waaaaaaaaaaaaaay more easier than class. I think they make it dificult on purpouse so they look smarter!
  Comment on PADAWAN's post “waaaaaaaaaaaaaay more eas...”
  (4 votes)
Rclxqvs_
Posted 4 months ago. Direct link to Rclxqvs_'s post “How do you do this with f...”
How do you do this with fractions? (I'm really bad with fractions and math)
Button navigates to signup pageComment on Rclxqvs_'s post “How do you do this with f...”
(10 votes)
Answer
- Kim Seidel
  Posted 4 months ago. Direct link to Kim Seidel's post “The process is no differe...”
  The process is no different. You replace each variable with its given value. Then you simplify the expression following order of operations rules and the rules for working with fractions. If you aren't great at working with fractions, then do yourself a favor and get more practice on that topic.
  Button navigates to signup page
  (9 votes)
Drunkenstein
Posted 4 years ago. Direct link to Drunkenstein's post “Does this topic have viab...”
Does this topic have viable application to non-Algebra subjects, if any? Thanx.
Button navigates to signup pageButton navigates to signup page
(9 votes)
Answer
- Kim Seidel
  Posted 4 years ago. Direct link to Kim Seidel's post “Absolutely! There are ma...”
  Absolutely! There are many formulas that get used in real life situations. This teaches you how to use a formula and calculate a result based upon replacing values into the formula.
  Comment on Kim Seidel's post “Absolutely! There are ma...”
  (17 votes)

MAP Recommended Practice

Course: MAP Recommended Practice > Unit 17

Evaluating expressions with one variable

How to evaluate an expression with one variable

Evaluating an expression with multiplication

New ways to show multiplication

Evaluating expressions where order of operations matter

Let's practice!

Challenge problems

Want to join the conversation?