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# 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 • When you first start learning math, the subtraction is always done with the 1st number larger than the 2nd number. So, your result is always a positive number.

When you start learning signed numbers, this changes. All those subtractions you've been doing are the same as adding a negative number. So, "subtract 1/6q" is the same as "adding negative 1/6q". You also learn that the sign in front of the number (the subtraction symbol) makes the number that follows it negative. This is why you will hear Sal use the 2 interchangeably.
"-1/6q" is "negative 1/6q", and it also is "subtract 1/6q".

Hope this helps.
• I miss Chuck Norris • Every time I think we're done with fractions, they come back to haunt me. • 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? • 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.
• 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? • anyone have a few brain cells to lend i dont understand this • Think about what you don't understand...

1) Do you know the difference between like and unlike terms? If not, then you should start back at the beginning of the lesson.

2) Did the addition/subtraction of decimals confuse you? If yes, then you should go to the Arithmetic course and review the lessons on working with decimal numbers.

3) Did the addition/subtraction of fractions confuse you? If yes, then you should go to the Arithmetic course and review the lessons on working with fractions.

If your confusion is due to something else, then please ask a more specific question so someone can assist you.
Hope this helps.
• 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? • 