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## Grade 7 (Virginia)

### Course: Grade 7 (Virginia)ย >ย Unit 1

Lesson 3: Adding & subtracting rational numbers# Adding & subtracting rational numbers: 79% - 79.1 - 58 1/10

Sal evaluates 79% - 79.1 - 58 1/10. Created by Sal Khan.

## Want to join the conversation?

- I still don't get how are you supposed to covert it into a fraction like you did in the video.(21 votes)
- i don know either i am confused(2 votes)

- How do you make a fraction a decimal?(8 votes)
- Divide the number on top of the fraction (the numerator) by the number on the bottom of the fraction (the denominator) and multiply by 100% (i.e. move the decimal point two places to the right and add a percentage sign).(18 votes)

- At1:41, Sal factors out a negative sign. Can someone explain to me what that it is and why he did it? Also, can you explain how they became positive? Thanks!(10 votes)
- ๐ ๐๐๐ ๐ข๐๐ ๐๐๐๐๐๐ ๐๐๐ ๐ ๐๐๐๐, ๐๐๐๐ ๐๐๐ ๐๐๐๐๐. ๐๐๐๐๐๐๐๐ ๐๐๐๐ ๐๐๐๐๐ ๐๐๐๐๐๐ ๐๐๐๐ ๐๐๐ ๐๐๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐. ๐๐๐๐๐ข ๐๐ ๐๐๐๐ ๐๐๐๐'๐ ๐๐๐๐.(4 votes)

- ๐ป๐๐ ๐น๐ ๐๐๐ ๐ป๐ถ๐ธ๐๐๐ ๐๐๐ ๐ถ ๐๐๐๐ถ๐๐พ๐๐ ๐๐พ๐๐?(9 votes)
- Essentially, to factor a negative number, find all of its positive factors, then duplicate them and write a negative sign in front of the duplicates. For instance, the positive factors of โ3 are 1 and 3.(6 votes)

- i thought when you change a subtraction sign to a plus sign then the number behind it would become negitive? Please explain this to me because this video just confused me?(5 votes)
- minusing a negative is the same thing as adding a positive(5 votes)

- This is so confusing! Can someone explain it with this question? I'm having a bit of trouble with this one;

-45/40 + 1.875=(5 votes)- First convert either of the numbers to the same format as the other one. E.g., decimal, fraction.

-45/40 = -1 5/40 = -1 1/8 = -1.125

Now solve the equation:

-1.125 + 1.875 = 1.875 - 1.125 = 0.75(2 votes)

- im confused why did he turn 79% into .79?(4 votes)
- Percent means you divide by 100, so then 79% would be 79/100 which is 0.79. Hope this helps.(4 votes)

- but why did he put it to adding and not subtracting instead?(4 votes)
- While I would not have done it this way because I have a very good sense of adding and subtracting numbers, the reason Sal factored out a -, thus changing all the signs, is because he saw that the two negatives would give a bigger answer than the positive number, and at this point in 7th grade, more people would do better to subtract a smaller number from a larger number, then just add the negative sign. I would tend to add the two negatives (if you have same signs, you add and keep the sign), so this would give .79 - 137.2, then subtract (opposite signs subtract and take sign of largest absolute value number) to get -136.41.

I really push learning these two addition/subtraction rules with my students over switching things around like Sal did.(4 votes)

- At1:25he talks about "factoring out" a negative sign what exactly is this and what is it used for?(5 votes)
- How do you calculate an addition/subtraction equation that starts with a negitive decimal and the rest are postive decimals?(3 votes)
- To give an example, are you talking about a question like this?

-.325 + .585?

If that is the case, then think of it like this. If the question is adding, and the negative decimal comes first, then do this. .585 -325. That should give you the answer.

If you are multiplying, such as this,

-.325 x .585

it's the same thing as multiplying negative numbers. Multiplying a negative number by a positive number will get you a negative number. So, do this. Take the decimals out, and multiply. You should get this equation.

-325 x 585= -190125.

Now, since you took 6 decimal places out, put 6 in. Your final answer should be -.190125.

If you are subtracting like this,

-.325 - .585,

that 585 will actually ADD to the negative -.325, making it -.910.

If you are dividing, think of it as the same thing as multiplying. Good luck!(6 votes)

## Video transcript

79% minus 79.1
minus 58 and 1/10. And I encourage you
to pause this video and try to compute this
expression on your own. Well, the thing that
jumps out at you is that these are in
different formats. This is a percentage. These are different
representations. There's a percentage. This is a decimal. This is a mixed number. And so to make sense of it,
it's probably a good idea to get them all in
the same format. And it seems like
we could get all of these into a decimal
format pretty easily. So let's go that way. So 79%, that literally
means 79 per 100. If you wanted to write it as a
fraction, it would be 79/100. But if you wanted to
write it as a decimal, it's 0.79, which could be 0-- or
we would write it down a 0.79. Now, 79.1 is already
written as a decimal, so we'll just write it again. So minus 79.1. And then, 58 and 1/10. Well, 1/10 is the
same thing as 0.1. So you could view this as 58--
well, and literally as 1/10. So it's minus 58 and 1/10. Or, you could view this as 58.1. So now they're all
in the same format, let's actually do
the computation. Now, the first thing
that jumps out at you is you have a fairly
small number here. Small positive number. It's less than 1. And you're subtracting fairly
large numbers over here. So your whole answer is
going to be negative. And to make sense of
this a little bit, what I'm going to
do is I'm going to factor out a negative sign. And that'll make
the computation-- at least in my brain, it's going
to make it a little bit easier. So if we factor out
a negative sign, this becomes-- so we're
going to factor it out. Actually, let me
just do it this way. So if we factor out
a negative sign, then this will become negative. This would be positive. And this would be positive. And just to verify this,
imagine distributing this negative sign, or
if this was a negative 1. Negative 1 times
this is positive. Negative 1 times
this is negative. Negative 1 times
this is negative. So these two expressions
are the exact same thing. And the reason why
I did that is now we'll do the more
natural thing of we will add these two numbers. We'll get a positive number,
a larger positive number than what we're going to
subtract from it right over here. So we can use our
traditional method. Although, we can't forget
about this negative out here. So let's first do that. Let's add 79.1 plus 58.1. So 79.1 plus 58.1. So 0.1 plus a 0.1 is 0.2. 9 plus 8 is 17. So that's seven 1's and one 10. So one 10 plus seven 10's
is going to get us to 0.8. Plus 0.5 gets us to
thirteen 10's, or 130. So we have 137.2 is this
part right over here. So 100. Let me write this down. So we have 137.2. And then from that,
adding a negative 0.79 is equivalent of
subtracting 0.79. So let's do that. Let's subtract
0.79, making a point to align our decimal points
so that we're subtracting the right place from
the right place. And now let's do
our subtraction. So right now we're
subtracting 9 from nothing. We could write a
0 right over here, but we still face an issue
in the hundredths place. We're also subtracting
a 0.7 from 0.2. So we're going to have
to regroup a little bit in the numerator in
order to subtract. Or at least, in
order to subtract using the most
traditional technique. So let's take a tenth from the
2, so it's only one tenth now, and give it to the hundredths. So one tenth is ten hundredths. So we could subtract that
ten hundredths minus nine hundredths is one hundredth. Now in the tenths place. We don't have enough up
here, so let's take 1 from the one's place. So that becomes a 6. 1 is ten tenths. So now we have 11 tenths. 11 minus 7 is 4. Add our decimal place. 6 minus 0 is 6. And then we got our
13 just like that. So outside the parentheses, I
still have the negative sign. When I computed all of this
inside the parentheses, I got 136.41. And then we can't forget about
the negative sign out here. So this whole thing
computes to negative 136.41.