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### Course: 7th grade (Eureka Math/EngageNY) > Unit 3

Lesson 1: Topic A: Use properties of operations to generate equivalent expressions- Intro to combining like terms
- Combining like terms with negative coefficients & distribution
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients
- Combining like terms with negative coefficients & distribution
- Combining like terms with rational coefficients
- Combining like terms with rational coefficients
- The distributive property with variables
- Factoring with the distributive property
- Distributive property with variables (negative numbers)
- Equivalent expressions: negative numbers & distribution
- Equivalent expressions: negative numbers & distribution
- Interpreting linear expressions: flowers
- Interpreting linear expressions: diamonds
- Interpreting linear expressions

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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?(73 votes)
- 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.(58 votes)

- 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?(37 votes)- 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.(55 votes)

- Every time I think we're done with fractions, they come back to haunt me.(38 votes)
- Omg, literally they always find their way back!(3 votes)

- 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(21 votes)- 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.(27 votes)

- 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..?(15 votes)
- 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 like0:52for 52 seconds into the video.(14 votes)

- 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?(10 votes)
- 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(13 votes)

- anyone have a few brain cells to lend i dont understand this(13 votes)
- 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.(9 votes)

- 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?(10 votes)- 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(11 votes)

- 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?(6 votes)- 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(15 votes)

- How does the teacher write so good on the PC😳(10 votes)
- Lots and lots of practice... lots...(5 votes)

## Video transcript

- [Voiceover] What I wanna do in this video is get some practice simplifying expressions and have some hairier numbers involved. These numbers are kind of hairy. Like always, try to pause this video and see if you can simplify this expression before I take a stab at it. All right, I'm assuming you have attempted it. Now let's look at it. We have -5.55 minus 8.55c plus 4.35c. So the first thing I wanna do is can I combine these c terms, and I definitely can. We can add -8.55c to 4.35c first, and then that would be, let's see, that would be -8.55 plus 4.35, I'm just adding the coefficients, times c, and of course, we still have that -5.55 out front. -5.55. I'll just put a plus there. Now how do we calculate -8.55 plus 4.35? Well there's a couple of ways to think about it or visualize it. One way is to say well this is the same thing as the negative of 8.55 minus 4.35, and 8.55 minus 4.35, let's see, eight minus four is going to be the negative, eight minus four is four, 55 hundredths minus 35 hundredths is 20 hundredths. So I could write 4.20, which is really just the same thing as 4.2. So all of this can be replaced with a -4.2. So my entire expression has simplified to -5.55, and instead of saying plus -4.2c, I can just write it as minus 4.2c, and we're done. We can't simplify this anymore. We can't add this term that doesn't involve the variable to this term that does involve the variable. So this is about as simple as we're gonna get. So let's do another example. So here I have some more hairy numbers involved. These are all expressed as fractions. And so, let's see, I have 2/5m minus 4/5 minus 3/5m. So how can I simplify? Well I could add all the m terms together. So let me just change the order. I could rewrite this as 2/5m minus 3/5m minus 4/5. All I did was I changed the order. We can see that I have these two m terms. I can add those two together. So this is going to be 2/5 minus 3/5 times m, and then I have the -4/5 still on the right hand side. Now what's 2/5 minus 3/5? Well that's gonna be -1/5. That's gonna be -1/5. So I have -1/5m minus 4/5. Minus 4/5. Now once again, I'm done. I can't simplify it anymore. I can't add this term that involves m somehow to this -4/5. So we are done here. Let's do one more. Let's do one more example. So here, and this is interesting, I have a parentheses and all the rest. Like always, pause the video. See if you can simplify this. All right, let's work through it together. Now the first thing that I want to do is let's distribute this two so that we just have three terms that are just being added and subtracted. So if we distribute this two, we're gonna get two times 1/5m is 2/5m. Let me make sure you see that m. M is right here. Two times -2/5 is -4/5, and then I have plus 3/5. Now how can we simplify this more? Well I have these two terms here that don't involve the variable. Those are just numbers. I can add them to each other. So I have -4/5 plus 3/5. So what's negative four plus three? That's going to be negative one. So this is going to be -1/5, what we have in yellow here. I still have the 2/5m, 2/5m minus 1/5. And we're done. We've simplified that as much as we can.