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Course: Integrated math 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 $\frac{1}{3}a-1-\frac{1}{2}b$ when $a=12$ and $b=6$.

Now, let's practice

Problem 1
Evaluate $\frac{3}{2}y-3+\frac{5}{3}z$ when $y=4$ and $z=3$.

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.
• why do we do this?
• You do this so that you can figure out how much of something there is when you have an unknown amount that can change.
• 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!
• How do i multiply 3/2 times 4
• 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.
• How is practice number 2 solved?
• 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.
• What's BEDMAS?
• BEDMAS is an acronym like PEMDAS to help you remember the rules for order of operations. The rules don't change.
• can somebody help me Evaluate 3/2 y - 3 +5/3 z when y=4 and z=3 like im just lost
• 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||
• 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.
• 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?