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## Algebra 1

### Course: Algebra 1>Unit 1

Lesson 3: Substitution and evaluating expressions

# 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.
Evaluating expressions with two variables: fractions & decimalsSee video transcript

## 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.
\begin{aligned} &\phantom{=}\dfrac13\blueD a-1-\dfrac12\goldD b \\\\ &= \dfrac13 \cdot \blueD {12}-1-\dfrac12 \cdot \goldD 6~~~~~~~~\text{Replace }\blueD{a} \text{ with } \blueD{12}\text{ and } \goldD b \text{ with } \goldD 6\text{.} \\\\ &=4 - 1 - 3 \\\\ &=0 \end{aligned}

## Now, let's practice

Problem 1
• Current
Evaluate start fraction, 3, divided by, 2, end fraction, y, minus, 3, plus, start fraction, 5, divided by, 3, end fraction, z when y, equals, 4 and z, equals, 3.

## Want to join the conversation?

• I really don't understand problem 1, could someone explain??
Why isn't it 0?
• 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)
(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.
• 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..
• 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.
• 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!
• 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!
• can somebody help me Evaluate 3/2 y - 3 +5/3 z when y=4 and z=3 like im just lost
• 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
• Several ways to do it, 3/2*4/1=3*4/2=12/2=6 or 3*4/2=3*2=6.
• How does one divide when one has 4(.5)
• I'm not quite sure I understand your question. Can you please rephrase it?
• 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
• 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.
• I dont understand problem 2. To be more specific I dont understand the fraction part 6(1/2). Could someone please help me.
• 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^