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## Get ready for Algebra 2

### Course: Get ready for Algebra 2>Unit 1

Lesson 1: Combining like terms

# Combining like terms with rational coefficients

Learn how to rewrite algebraic expressions by combining like terms. The expressions in this video have decimal and fraction coefficients.

## Want to join the conversation?

• Can a whole number be distributed to a decimal with a variable?
• So you are saying something like 4 (.5x)? Yes distribution is based on multiplication, so 4*.5 = 2, final simplification would be 2x. If you did 5(.5x) you would end up with 2.5x.
• Following this video I did the challenge which asked:

-3.6 - 1.9t + 1.2 + 5.1t

I gave the answer 2.4 - 3.2t, since we start with the number "-3.6", however I was told this was wrong and that this was the solution:

#1/3
Combine the coefficients of the t terms, and combine the constant terms.

#2/3
= -3.6 - 1.9t + 1.2 + 5.1t
= (-1.9 + 5.1) ⋅ t - 3.6 + 1.2
= (3.2) ⋅ t - 2.4
= 3.2t - 2.4

#3/3
The simplified expression is 3.2t - 2.4

Why is the answer not the other way around? We start with -3.6 and so why doesn't the number without the variable come first in the simplified expression too?
• It doesn't really matter whether the number with or without the variable comes first. The answer can also be written as -2.4 + 3.2t. What you need to remember is that each negative sign is attached to the number to the right of it.
The original thing can be rewritten as:
(-3.6) + (-1.9t) + 1.2 + 5.1t

I honestly don't like the way they explained it. It seems like it overcomplicates things. You just have to remember that the minus signs are not free floating. They're each connected to a number.

Hope this helps :)

Edit:
Looking back on this answer a year later, and I realize I should have mentioned that in standard form, the number with the variable always comes first. -2.4 + 3.2t and 3.2t - 2.4 mean the same thing, but if you want to be picky about it, 3.2t - 2.4 is in standard form.
• Please answer my question... I'm desperate. Sometimes during math I will see a problem and it says something like
**11/12 - 1/6q + 5/6 -1/3
Then I figure out my answer and ask if its correct and then my teacher will say that its wrong because somehow 1/6q is negative because is being subtracted by 11/12. Now I'm getting confused because Sal keeps on saying negative when he means subtraction...or does he? He'll say negative 4/5 but when he writes it down its just minus 4/5. Can someone please explain this to me. It doesn't make sense. Why would 1/6q be negative and how? Is this some new thing now that every number that has a subtraction sign in front of it is negative or has it been that way all along and never really mattered until now I can't level up in this whole combining like terms section cuz the potato who made algebra decided he wanted to. Can someone explain to me what this negative minus mishap stupid algebra thing is
• It would equal -7
(1 vote)
• i came across a problem which was simplify 3.4-2.8d+2.8d-1.3 and the answer i got was 2.1 - 5.6d, and it keeps telling me that i may have use the wrong letters. What am i doing wrong?
• the wrong thing is that you're adding them instead of subtracting.
(plus)*(minus) is minus. so when you subtract them, you are left with nothing, but only 2.1
• In Practice: Combining like terms with negative coefficients, I think the answer to the question that reads, '''−3x−6+(−1)''' is x = -5/3, but the practice checking thing keeps saying I am wrong. could you help?

here's what I did.
−3x−6=−1
−3x−6+6=−1+6
−3x=5
−3x/-3 = 5/-3
x = -5/3
isn't that correct?
• is −3x−6+(−1) equal to 0? If there is no equal sign you can't insert one. Instead you just combine like terms which it looks like you have a handle on. The only like terms I see are -6 and -1
• In the first problem why does he put the coefficients with the variables last when he presents the answer. The pattern I have observed as I have worked through these problems is that it always gets put in the first part of the answer. Also why does he put a "plus" sign after 5.55 (@0.52), this all seems inconsistent to me..?
• The order in which the variables with coefficients go does not matter when you are adding or subtracting (PEMDAS). So the pattern that you have observed is just because of a personal preference towards putting the coefficients at the start. Sal probably put the variables last in order to group up the variables together so that it will be easier for people to follow what he does in the following step.

For the second part of your question, Sal puts the plus sign after the 5.55 as the value is being added to the remaining part of the equation. Try distributing the 'C' into the parentheses and you will find that both equations are equivalent.

Also, if you want to refer to a specific part of the video, just write it out like for 52 seconds into the video.
• I had the same thing as Jeremy Hunter

Following this video, I did the challenge which asked:

-3.6 - 1.9t + 1.2 + 5.1t

I gave the answer 2.4 - 3.2t since we start with the number "-3.6", however, I was told this was wrong and that this was the solution:

#1/3
Combine the coefficients of the t terms, and combine the constant terms.

#2/3
= -3.6 - 1.9t + 1.2 + 5.1t
= (-1.9 + 5.1) ⋅ t - 3.6 + 1.2
= (3.2) ⋅ t - 2.4
= 3.2t - 2.4

#3/3
The simplified expression is 3.2t - 2.4

Why is the answer not the other way around? We start with -3.6 and so why doesn't the number without the variable come first in the simplified expression too?
• Great question. In fact, it would absolutely work if you put it the other way around. In that case, it would be:
-2.4 + 3.2t
You might notice that it is different from your answer of 2.4 - 3.2t. That is because you made a mistake with the negative signs.
That question can be rewritten as (-3.6)+(-1.9t)+1.2+5.1t. This works because adding a negative number is the same thing as subtracting that number. Now, you can combine the like terms.
-3.6+1.2 and -1.9t+5.1t.
That would give you -2.4+3.2t
• Just wanted to ask for example, why do I have to reduce 4/6 to 2/3? don't they equal the same? someone please kindly explain why I have to reduce? Thanks :)
• Yes, 4/6 is equal to 2/3. But, we always reduce fractions to their simpliest form. It makes them easier to work with in reduced form.
• i still dnot understand how to do it is there an easier step to get the answer
• Let me explain.
Let´s say our problem was:

5x+3-2+10-8x=30x

I see that there are some terms I can combine. On the left side of my equation, I have 5x, +3, -2, +10, -8x. I have a lot of the same term.

5x-8x=-3x
3-2+10=11

Now the left side of my equation reads:

-3x+11=30x
I need to carry the -3x to the right side of the equation to pair I with 30x. When you carry it over, it becomes positive.

30x+3x=33x

33x=11
x=3

I really hope this clears up!