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## 7th grade

### Unit 3: Lesson 2

Adding & subtracting rational numbers# Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150%

Sal evaluates 0.79 - 4/3 - 1/2 + 150%. Created by Sal Khan.

## Want to join the conversation?

- i dont get how he turned 550 and 450 into -100 then turned it into 137(3 votes)
- He Subtracted those two number and got - 100(6 votes)

- Thank you, This video helped me so much! :)(9 votes)
- why did you multiplied the 100 by 3 so it become 300 ?(8 votes)
- In order to add or subtract fractions you have to first put them over the same denominator. For example you can't add 1/2 and 1/4 because they have a different denominator (the 2nd number in each fraction), so you have to first convert the fractions to use the same denominator (a 'common denominator').

After you have given them the same denominator (see link below on how to do this) you can simply add the numerators: 2/4 + 1/4 = 3/4

See this video for more information: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-fractions-topic/cc-5th-add-sub-fractions/v/adding-fractions-with-unlike-denominators(2 votes)

- I got 100% on the math lesson that my teacher gave me before.(8 votes)
- can someone explain the whole simplifying the fractions bit, im so confused(3 votes)
- So you have a
**LARGE**fraction: 80/100

To make it smaller you divide by a number.

But what number?

Well, I know that 80 and 100 are divisible by 10.

so: 80/10 divided by 10 = 8/10

Unlike whole numbers, the larger the denominator of the fraction is, the smaller the units are(3 votes)

- Any reason to not write 150% as a mixed number? 1 1/2?(2 votes)
- You could do that, but it is easier to work with the numbers when you have it as an improper fraction. The other reason is Sal is trying to get a
**common denominator**so that he can add/subtract all of the expressions.(2 votes)

- this problem 1/2 −60%−25% should solve as in i have half pizza, i eat 60% of that half, then i eat 25% of whats left so i still have 0.15 of that half pizza.

why does Sal turn it into 0.5−0.6−0.25=−0.35 as the solution? and how do i know when to solve it one way and when to solve the other way?(2 votes)- Well, if 1∕2 represents half a pizza, then 60% of half a pizza would be equal to 60%∙(1∕2)

But, we don't have 60%∙(1∕2), we have 60%, which we can write as 60%∙1 = 60% of a*whole*pizza.

And of course, taking away 60% of a pizza from half a pizza lands us at −10% of a pizza.

Taking away another quarter pizza leaves us with −35% of a pizza.(2 votes)

- I Don't understand any of this! D: SOMEONE EXPLAIN IT PLEASE!!(2 votes)
- Can you be more specific? Give an example of a problem that's causing you grief, and I'm happy to work it here in the comments.(2 votes)

- Who's afraid of fractions?!
`0,79-4/3-1/2+150%`

=79/100-4/3-1/2+150/100

Solve for x:`3*x=100`

x=100/3

Convert 100/3 to mixed number:`33+1/3`

`79/100-(4*(33+1/3))/(3*(33+1/3))-(1*50)/(2*50)+150/100`

=79/100-(132+4/3)/100-50/100+150/100

=(79-132+4/3-50+150)/100

=(-53+100+4/3)/100

=(47+4/3)/100≈(48,33)/100≈0,483

If you want exact fraction as answer you will have to work some more on it:`(47+4/3)/100`

=(141/3+4/3)/100

=(145/3)/100

=(145/3)*(1/100)

=145/300

=(145/5)/(300/5)

=29/60

≈0,483333333.........

Who's afraid of fractions?! This is a really fun exercise! It jogs your memory and you get to use all the things you know about adding and subtracting fractions, converting decimals, converting percents, converting mixed numbers, and even doing approximations with repeating decimals and rounding and doing looong divisions and division tests.

Is this hard?... well yes, it's a challenge for anyone, and it's hard not to make a mistake, but it's a hell of a fun and it's supposed to be hard if you want to push yourself to the limit. Personally, for me that's the only way to learn. Of course you have to do it step by step, and learn the basics first. But it's a great satisfaction when you get it right.

Update:

I know where I made my mistake now. I did a sign error when I put all the numerators on the same fraction bar. This is why mixed numbers are up to no good. I hate mixed numbers. They are counter-intuitive and they just mess it up for me. I prefer improper fractions rather. So here is the correct answer.`0,79-4/3-1/2+150%`

=79/100-(4*(33+1/3))/(3*(33+1/3))-(1*50)/(2*50)+150/100

=79/100-(132+4/3)/100-50/100+150/100

This is the step at which I made a mistake:`right: (79-(132+4/3)-50+150)/100=0,4567`

wrong:(79-(132-4/3)-50+150)/100=0,4833

Notice the difference at the second term in the numerator. If you copy and paste the first line in a calculator on your computer you should get the right approximation, which is 0,4567.

But anyway! Here is the rest of the calculation.`=(150-50+79-(132+4/3))/100`

=(179-132-4/3)/100

=(47-4/3)/100

=((47*3)/(1*3)-4/3)/100

=((141)-(4/3))/100

=(137/3)/100

=(137/3)*(1/100)

=137/100

So there you go! The same result as Sal got using the simple method. The idea is the same, you have to put every fraction in terms of the same denominator. Sal used the least common multiple of 100, 3, and 2. That's 300. I used the multiple 100, which is not common among all three numbers. That's why the calculation was more complicated. But I just had to try it out and prove it to myself that it works. And it does, as long as you don't make mistakes along the way like I did.

I am still not afraid of fractions! ;) Not even the mixed number type of fractions... those weird looking things.(3 votes) - how do you know what 150% means, 150% of what?(1 vote)
- When working with percentages we're always doing a percentage of one whole. Specific units won't change the result, we can just say that 150% is equal to 1.5 of one whole
*______*(unit)(2 votes)

## Video transcript

So we have 0.79 minus
4/3 minus 1/2 plus 150%. So we have four
different numbers written in different formats. Here it's a decimal, here
we have two fractions, and then here we
have a percentage. So the easiest
thing to do would be to write all of these
in the same format. And for me, the easiest format
to do this computation in would be to write
them all as fractions. And the reason why I want to
do that, in particular, is because 4/3, when you divide
by 3, when you divide 1/3, 2/3, 4/3, you're going to
have a repeating decimal. So to avoid that,
I want to put all of these-- I want to rewrite
all of these as fractions. So let's do them one at a time. So 0.79, this is the
same thing as 79/100, so I'll just write it that way. So this is the same
thing as 79 over 100. Then of course,
we have minus 4/3. Then we have minus 1/2. And then finally,
we have-- I don't want to run out of colors here. Finally we have 150%. Well, 150%, percent literally
means per cent, per hundred. So this is plus 150 per 100. So now we've written
them all as fractions. And in order to do all the
subtraction and addition, we have to find a
common denominator. So what's the least common
multiple of 100, 3, 2, and 100? Well, 100 is divisible
by 2, so 100 is actually the least common
multiple of 102. So we really have to just
find the least common multiple between 100 and 300. And that's just going to be 300. There's no other common
factors between 100 and 3. So let's write all of them with
300 as the common denominator. So let me do this in
this reddish color. So 79 over 100 is
the same thing. If I were to write it over
300, to go from 100 to 300 in the denominator,
I'm multiplying by 3, so I have to multiply the
numerator by 3 as well. So I'm going to multiply
it by 3 as well. Let's see, 80 times
3 would be 240. So it's going to be
3 less than that. So 240 minus 3 is 237. Now 4/3. Well, to get the
denominator to be 300, we have to multiply
the denominator by 100, so we have to multiply the
numerator by 100 as well. 1/2, if our denominator is 300,
we multiplied the denominator by 150 to go from
200 to 300, so we have to multiply the
numerator by 150. And then finally, 150
over 100, well, we're multiplying the
denominator by 3 to get to 300, to go from 100 to 300. So we have to do the same
thing in the numerator. So 3 times 150 is 450. So now we have the
same denominator, and we can now add
our numerators. So this is going to be
equal to-- actually, I could just do it right over
here on the right-hand side. This is going to be equal
to some stuff over 300. So it's going to be 237
minus 400 and minus 150 and-- this actually should
be a plus right over here. This should be plus 450. And so let's see if we could
simplify this a little bit. We're subtracting 400,
and we're subtracting 150. So these two would be the
same thing as subtracting 550. And then we have a
positive 237, and we're adding it to a positive 450. Or actually, maybe
another easier way to think about this is
negative 550 plus 450 is going to get us negative 100. And so this simplifies
things a good bit. Now we have 237 minus
100 is going to be 137. So it equals 137 in
the numerator over 300. And this is about as simplified
as I can think of making it. And so this is our
final answer, 137/300.