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## Algebra 1

### Course: Algebra 1 > Unit 1

Lesson 3: Substitution and evaluating expressions- Evaluating expressions with two variables
- Evaluating expressions with two variables
- Evaluating expressions with multiple variables
- Evaluating expressions with two variables: fractions & decimals
- Evaluating expressions with two variables: fractions & decimals
- Evaluating expressions with multiple variables: fractions & decimals

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# Evaluating expressions with two variables: fractions & decimals

Evaluating expressions with two variables involves substituting the given values for each variable and simplifying the expression. By practicing with examples, we can improve our skills in solving these types of problems, ultimately enhancing our understanding of algebraic expressions and their real-world applications.

## Want to join the conversation?

- at1:03in the video he says if we get half of 7 we get 3.5 but how does he get the that?(23 votes)
- The decimal representation of 1/2 is 0.5, which is what he uses in the video.

He wrote 0.5 and says "one half", since they a representations of the same thing.

Hope that helped.(36 votes)

- Why does Sal halve 7 when he multiplies it by 0.5?(8 votes)
- because if you multiply anything by any value less than 1, it gets necessarily cut in half.(10 votes)

- Can someone help me? The video didn't help me and i am struggling.(9 votes)
- What do you need help with?(4 votes)

- i dont understand how 12 (1/4) equals 3 can someone help(6 votes)
- 12 in fraction form is 12/1

Multiply 12/1 (1/4) = (12*1)/(1*4) = 12/4 = 3

Hope this helps.(6 votes)

- okay just in case anyone (like me on several occasions) has forgotten, here's a quick way to multiply numbers with decimals:

- 1. ignore the decimal point and turn it into a regular number

- 2. multiply that with the other number

- 3. count how many numbers are behind the decimal point

- 4. move the decimal point across in your answer that many digits

- 5. boom, there's the answer

e.g. 9 x 4.5

- 1. 4.5 to 45

- 2. 9 x 45 = 405

- 3. there is 1 number behind the decimal point in 4.5

- 4. 405 becomes 40.5

- 5. the answer is 40.5

there.

to whoever finds this useful, you're welcome :)(8 votes)- As a graduating senior I thank you for reminding me of such a useful tip lol(0 votes)

- why do you have to make 0.25 a fraction?(4 votes)
- You don't. 8(0.25) = 2, so you get the same result in decimal form.(4 votes)

- How did 7x0.5=3.5?

How did 8x0.25=2?(4 votes)- Seems like you to need to review the lessons for multiplying with decimal numbers.

7x0.5 = 3.5 because 7x5=35 and the answer needs 1 decimal place given that there is one decimal place in the original number.

0.7x0.5 = 0.35 because now the original 2 numbers have 2 decimal places in total. So, the answer requires 2 decimal places.

8x0.25 = 2 because 8x25 = 200 and the result needs 2 decimal places due to the 2 decimal places in the original numbers. This change the 200 into 2.00 or just 2.

See lessons at: https://www.khanacademy.org/math/algebra-basics/basic-alg-foundations/alg-basics-operations-with-decimals/v/multiplying-decimals(4 votes)

- I don't really get it and i watched this video 3 times already... :/(1 vote)
- It would be helpful if you said what you found confusing or what you didn't understand. You need to understand several basic concepts to understand this video. Those concepts are listed below. I encourage you to look through them and try to isolate what is confusing you and review the appropriate topic(s). Then, come back and try this video again.

1) Basic Substitution: The process in the video is no different than if you substitute whole numbers or integers for the variables. So, this video assumes you understand the basic concepts for substitution. If you won't understand that, try reviewing the prior section starting with this video and working forward to the one you found confusing. Prior section is at: https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-intro-to-variables/v/variables-and-expressions-1

2) Order of Operations (PEMDAS): Once numbers have replaced the variables by using substitution, you need to know the rules for order of operations. If you need a review of that concept, go here: https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/algebra-foundations-order-of-operations/v/introduction-to-order-of-operations

3) Operations involving Decimals and Fractions: Lastly, you need to know how to add, subtract, multiply and divide decimals and fractions. If you don't know how to do any of these, you need to review those topics. Here is link to section on decimals: https://www.khanacademy.org/math/algebra-home/pre-algebra/decimals-pre-alg

Here is link to section on fractions: https://www.khanacademy.org/math/algebra-home/pre-algebra/fractions-pre-alg(8 votes)

- 2:56Can you explain how you got the answer? How do you caculate 0.25(also 1/4) multiply 12? The 12(1/4)(2 votes)
- You multiply 0.25 or 1/4 or 25/100 times 12 and that = 3.(6 votes)

- what is 3.10+7-2(3 votes)
- Follow order of operations rules (PEMDAS). If you used the period to indicate multiplication, then multiply first. Then add/subtract from left to right to get your final result.

If the period is a decimal point, then just add/subtract from left to right.

Hope this helps.(4 votes)

## Video transcript

- [Voiceover] Let's see
if we can give ourselves some practice evaluating expressions that have two different variables in them So let's see if we can
evaluate the expression seven J plus five minus eight K, when J is equal to 0.5
and K is equal to 0.25. So why don't you try to pause the video and evaluate this first before
we work through it together. Alright, so if we want
to evaluate this thing, everywhere we see a J we
want to replace it with a 0.5 and everywhere we see a K we want to replace it with a 0.25, so let's do that. This is going to be seven times, and instead of J I'm gonna put a zero, a 0.5 in there. And then we have plus five minus eight times K. And K we're saying is 0.25. 0.25. So what is this going to be equal to? So if I were to take, if I were to take, and I can color code this, seven times 0.5. Half of 7, that's going to
be three and a half, 3.5. Then I have plus five. And then I'm gonna subtract. I am subtracting eight times 0.25. 0.25, this is 1/4. I could rewrite this if I want. 0.25, that's the same thing as 1/4. Eight times 1/4, or another
way to think about it is eight divided by four is
gonna be equal to two. So this whole thing over here
is going to be equal to two. So it's gonna be minus, we
have this minus out here, so minus two. And what is this going to be? Well, let's think about it. 3.5 plus five is 8.5, minus two is going to be 6.5. So this is equal to this, is equal to 6.5. Let's do another one of these. Alright. And we'll, just like before, try to work through it on your own before we do it together. Alright, now let's do it together. So over here I have this expression 0.1 M plus eight minus 12 N, when M is equal to 30
and N is equal to 1/4. Alright. So everywhere I see an M I
want to replace with a 30. And everywhere I see an N I
want to replace with a 1/4. So this is going to be equal to 0.1 times M. M is 30. Times 30 plus eight minus 12 times N, where N is 1/4. N is 1/4. So what is, what is 1/10, This right over here,
0.1, that's the same thing as 1/10 of 30? Well 1/10 of 30, that's going to be three. So this part is three. And we have three plus eight. And then we're gonna have minus. Well what is 12 times 1/4? That's gonna be 12/4,
or 12 divided by four, which is going to be equal to three. And now when we evaluate this, so that is equal to this, we have three plus eight minus three. Well, threes are going to, you know positive three, then
you're gonna subtract three, and you're just going to be left with, you're just going to
be left with an eight. And you're done. This expression when M is equal
to 30 and N is equal to 1/4 is equal to eight.