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### Course: 6th grade > Unit 6

Lesson 5: Evaluating expressions with multiple variables- Evaluating expressions with two variables
- Evaluating expressions with multiple variables
- Evaluating expressions with two variables: fractions & decimals
- Evaluating expressions with multiple variables: fractions & decimals
- Evaluating expressions with two variables
- Evaluating expressions with two variables: fractions & decimals

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# Evaluating expressions with two variables

Evaluating expressions with multiple variables involves substituting given values for each variable and simplifying the expression. By replacing variables with their corresponding values, we can easily compute the result of expressions, even for more complex examples with multiple terms and operations. Created by Sal Khan.

## Want to join the conversation?

- For the second expression, 3(2)-2+3(3)= 5 not 13

I thought you were suppose to add before you subtract?(55 votes)- (1.) 3(2) - 2 + 3(3) (Multiply 3 by 2 and 3 by 3 because multiplication comes before addition or subtraction.)

(2.) 6 - 2 + 9 (Because we move from left to right, we subtract first.)

(3.) 4 + 9 = 13(19 votes)

- I thought PEMDAS is applied to Algebra? The last example that Sal gave made me confused. Can someone help me?(33 votes)
- MD (Multiplication and Division) and AS (Addition and Subtraction) go left to right. If a division problem comes before a multiplication problem, you do the division first.(23 votes)

- What does it mean when numbers are in parentheses?(18 votes)
- That means that you simply need to do the math inside those parentheses first.

Example:

2 + 3 * 5 = 2 + 15 = 17

(2 + 3) * 5 = 6 * 5 = 30(22 votes)

- When the equation comes to "6 - 2 + 9" would the answer not be minus 5? should you not add 9 and 2 and then subtract because of the order of operations ?(12 votes)
- This can be a common misunderstanding of the "order of operations" if you are using a mnemonic to remember them by. Multiplication and Division happen at the same time, not multiply first, then divide, and the same for addition and subtraction. You don't do all the adding and then do all the subtraction, you do them at once (unless there are brackets/parenthesis of course).

So in this case, it is

6 plus -2 plus 9 and you can put those in any order too

9 plus 6 plus -2 / -2 plus 9 plus 6 / -2 plus 6 plus 9 etc.(21 votes)

- Can somebody explain the PEMDAS(8 votes)
- P - Parenthesis

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

The order of which you solve an equation.(25 votes)

- can i write the dot which represent (x)times on any topic(10 votes)
- Yes, it is just another way of showing multiplication.(12 votes)

- So do we do BEDMAS to work out the answer or just the order of expressions?(9 votes)
- PEMDAS is only used to work out the order of operations, or which expressions to calculate first.(11 votes)

- I'm so confused. HOW are you deciding what numbers each of the letters are? How are you deciding the a=7, b=2, x=3 and y=2?(10 votes)
- In this situation, he's pretty much just picking random numbers. He's just showing you the concept so that when you do more complicated stuff, and have exact values for the variables, you'll know how to plug them into equations :)(4 votes)

- Say X is 45 and Y is 5 what would you get X+Y?(6 votes)
- Plug in the values and you'll get 45 + 5 which is 50.(10 votes)

- Why do you not have to do all the addition first in this? I got 13 first but then saw I did the addition after doing the subtraction.(5 votes)
- The order of operations rules tell us to add/subtract working left to right. They do not say to do all addition first.

Hope this helps.(10 votes)

## Video transcript

Now, let's think
about expressions with more than one variable. So say I had the
expression a plus-- I'll do a really
simple one, a plus b. And I want to evaluate this
expression when a is equal to 7 and b is equal to 2. And I encourage you to pause
this and try this on your own. Well, wherever we see
the a, we would just replace it with the 7. And wherever we see the b,
we'd replace it with the 2. So when a equals
7 and b equals 2, this expression
will be 7 plus 2, which, of course, is equal to 9. So this expression
would be equal to 9 in this circumstance. Let's do a slightly
more complicated one. Let's say we have the expression
x times y minus y plus x. Actually, let's make it plus 3x. Or another way of saying
it plus 3 times x. So let's evaluate this when x is
equal to 3 and y is equal to 2. And once again, I encourage
you to pause this video and try this on your own. Well, everywhere we see an
x, let's replace it with a 3. Every place we see a y,
let's replace it with a 2. So this is going to
be equal to 3 times y. And y is 2 in this case. 3 times 2 minus 2
plus this 3 times x. But x is also now equal to 3. So what is this
going to be equal to? Well, this is going to be
equal to 3 times 2 is 6. This 3 times 3 is 9. So it simplifies
to 6 minus 2, which is 4, plus 9, which
is equal to 13. So in this case,
it is equal to 13.