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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: fractions & decimals

We've already evaluated expressions with two variables. Now it's time to do it with fractions and decimals.

## Let's study another example.

**Evaluate**$\frac{1}{3}}a-1-{\displaystyle \frac{1}{2}}b$ when $a=12$ and $b=6$ .

## Now, let's practice

## Want to join the conversation?

- I really don't understand problem 1, could someone explain??

Why isn't it 0?(20 votes)- I'm going to assume you mean problem 1 in "let's practice" rather than the 1st problem in the video or just below the video.

Problem 1 in practice is: (3/2)y-3+(5/3)z given the values of y=4 and z=3

Substitute the vales for the variables:

(3/2)(4/1)-3+(5/3)(3/1)

Follow PEMDAS rules. Multiply first.

(3/2)(4/1)=12/2=6

(5/3)(3/1)=15/3=5

So, the expression is now: 6-3+5

Now, add and subtract from left to right.

6-3+5 = 3+5 = 8

The answer is 8. Why do you think it should be 0?

Hope this helps.(121 votes)

- Why is the answer to the second question 11? If I follow the order of operations shouldn't the answer be 5? Do addition first.. so 5 + 3 = 8.. then subtraction 13 - 8 = 5..(13 votes)
- You aren't quite following order of operations. In PEMDAS, there are 4 steps, not 6.

P = Parentheses: Do any work inside first

E = Exponents: Do any exponents or radicals next

MD = Multiply & Divide: These are one step. You need to work them from left to right

AS = Add & Subtract: These are one step. Again, you need to work them from left to right

So, when applied to the 2nd problem: 13-5+3

You go left to right: 13-5=8

Then 8+3=11

Hope this helps.(81 votes)

- why do we do this?(15 votes)
- You do this so that you can figure out how much of something there is when you have an unknown amount that can change.(6 votes)

- Wait, so, the first practice question has 3 over 2, isn't that an improper fraction? Am I supposed to treat it as an improper fraction and divide 3 into 2? Or, do I treat it as a normal fraction and try and figure out the problem? When I try to divide 3 into 2, i get 0.666... and so on. Thanks!(7 votes)
- It's good that you saw that the answer 0.666... does not make good sense for the improper fraction 3 over 2. This should tell you that dividing 3 into 2 is an incorrect method.

The fraction 3 over 2 actually means dividing 2 into 3. You should get 1.5 for the fraction 3 over 2.

In general, the fraction a over b means dividing b**into**a, or equivalently dividing a**by**b.

Have a blessed, wonderful day!(13 votes)

- How do i multiply 3/2 times 4(2 votes)
- Change 4 into a fraction: 4/1

To multiply fractions, you multiply numerator to numerator and denominator to denominator.

3/2 * 4/1 = (3*4)/(2*1) = 12/2

Then, reduce the fraction to 6

Hope this helps.

FYI - You may want to get more practice working with fractions. The lessons from here assume you know how to work with them.(23 votes)

- How is practice number 2 solved?(5 votes)
- 1) Replace each variable with its given value.

13-0.5(10)+6(1/2)

2) Follow order of operations rules (PEMDAS)

-- Multiply: 13-5+3

-- Add & subtract: 13-5+3 = 8+3 = 11

Hope this helps.(17 votes)

- What's BEDMAS?(7 votes)
- BEDMAS is an acronym like PEMDAS to help you remember the rules for order of operations. The rules don't change.(11 votes)

- can somebody help me Evaluate 3/2 y - 3 +5/3 z when y=4 and z=3 like im just lost(6 votes)
- 3/2y-3+5/3z y=4 z=3

3/2*4/1-3+5/3*3/1

12/2-3+15/3

6-3+5=8

||I was thinking it is solved this way||(2 votes)

- I am a bit stuck. how do we do 3/2 • 4 and 5/3 • 3

? Please help!(4 votes)- Several ways to do it, 3/2*4/1=3*4/2=12/2=6 or 3*4/2=3*2=6.(7 votes)

- Why isn’t the answer tho the first “let’s practice” problem 14? I’ve went back to check if any mistakes had occurred but I found 0. Why isn’t it 14?(2 votes)
- Replace each variable with their given value:

3/2(4) - 3 + 5/3(3)

Follow order of operations rules

Multiple: 12/2 - 3 + 15/3

Divide: 6 - 3 + 5

Add/subtract from left to right:

6-3+5 = 3+5 = 8

To get to 14, you must have added the 3 instead of subtracting it.

Hope this helps.(10 votes)