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# 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
• He Subtracted those two number and got - 100
• Thank you, This video helped me so much! :)
• why did you multiplied the 100 by 3 so it become 300 ?
• I got 100% on the math lesson that my teacher gave me before.
• can someone explain the whole simplifying the fractions bit, im so confused
• 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
• Any reason to not write 150% as a mixed number? 1 1/2?
• 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.
• 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?
• 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.
• I Don't understand any of this! D: SOMEONE EXPLAIN IT PLEASE!!
• 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.
• 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=100x=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=0,4567wrong:(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.