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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

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 start fraction, 1, divided by, 3, end fraction, a, minus, 1, minus, start fraction, 1, divided by, 2, end fraction, b when a, equals, 12 and b, equals, 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?(15 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.(69 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..(9 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.(52 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!(6 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!(7 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)
- hi, this is how you solve it when y=4 and z=3

3/2 y - 3+5/3z (substitute letters)

3/2 times 4 - 3+5/3 times 3

6 - 4-4+ 5/3 times 3

6-4-4+5

2-4+5

-2+5

3

so, the answer is 3. hope this helps!(1 vote)

- 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)

- How does one divide when one has 4(.5)(4 votes)
- I'm not quite sure I understand your question. Can you please rephrase it?(5 votes)

- on the last step why was he able to eliminate posative 3 and negative 3? so quick without going through pemdas i know it will come out to 8 either way but did you use a faster way to get the answer? = 3 + 8 - 3(5 votes)
- It's a faster way: 3 + 8 + (-3). Commutative Property:

3 + (-3) + 8. 3-3 = 0. 0 + 8 = 8.

Or you can just mental math it and cancel out the 3 without rearranging the equation.(4 votes)

- I dont understand problem 2. To be more specific I dont understand the fraction part 6(1/2). Could someone please help me.(5 votes)
- Hey! To put it simply you just have to divide 6 by 2 to cut it in half in 13 - 0.5w + 6x when w =10 and x = 1/2. That makes the expression 13 - 5 + 3 = 11 if you follow PEMDAS.

Hope this helps! ^o^(4 votes)

- the answer. i need it. It won't let me type in fraction(4 votes)
- When typing fractions onto spaces when inputting answers's questions, try using the "slash" symbol, /,or the fraction command inside the pop-out menu.(6 votes)

- evaluate (3/2)y - 3 + (5/3)z when y = 4 and z = 3

how come we add 4(y) and 2 instead of multiplying

and

how come we cancel out the two 3s and keep the 5 instead of multiplying(1 vote)- you do multiply not add(1 vote)