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### Course: 6th grade (Illustrative Mathematics)>Unit 6

Lesson 19: Extra practice: Expressions

# 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?

• at in the video he says if we get half of 7 we get 3.5 but how does he get the that?
• 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.
• How does this type of pb solving resolve real world dilemmas??
• There are many formulas used in the real world, perimeter, area, compounded interest, tax calculations, etc. Formulas use variables. If you want to use the formula, you need to know how to replace the variables with the appropriate values and do the math. The values given to the variables could be decimals, fractions, mixed numbers, etc. The formula could have a fraction or a decimal.
• Why does Sal halve 7 when he multiplies it by 0.5?
• because if you multiply anything by any value less than 1, it gets necessarily cut in half.
• Can someone help me? The video didn't help me and i am struggling.
• It's Basically substitution
• i dont understand how 12 (1/4) equals 3 can someone help
• 12 in fraction form is 12/1
Multiply 12/1 (1/4) = (12*1)/(1*4) = 12/4 = 3
Hope this helps.
• PEMDAS or GEMDAS always applies whenever you do something like this, right? I hope I'm right.
• Yes, the order of operations rules always apply in problems like these.
• When we say decimals isn't the decimals said as for example 0.45 said as 0 and 45 hundredths?
• You can say it that way. Or, you can just say: 45 hundredths.
• why do you have to make 0.25 a fraction?
• You don't. 8(0.25) = 2, so you get the same result in decimal form.
• how do you subtract first then add ? it doesnt make sense when you your using the P.E.M.D.A.S method . this website has the answer backwards . i got half my answers wrong cause you guys subtract then add which is the other way around
• PEMDAS has 4 rules / steps, not 6.
P = First, do any work inside parentheses or other grouping symbols.
E = Do exponents and radicals 2nd.
MD = Multiply and Divide are one rule/step. We work them from left to right.
AS = Add and Subtract are also one rule/step. We work them from left to right.

This is why the subtraction is being done before the addition in the video. The subtraction is on the left, so it comes first.

Hope this helps.
• at in the video he says if we get half of 7 we get 3.5 but how does he get the that?
• you multiply 7 and 0.5 that would give you 3.5 when a number is but into a decimal like 0.5 for example it become half of the number when multiplying just like 12 times 0.5 it become 6

## 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.