If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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?

  • piceratops sapling style avatar for user jaydajazz
    i dont get how he turned 550 and 450 into -100 then turned it into 137
    (3 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user Tristan G.
    Thank you, This video helped me so much! :)
    (9 votes)
    Default Khan Academy avatar avatar for user
  • leaf green style avatar for user Aways
    why did you multiplied the 100 by 3 so it become 300 ?
    (8 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Priscilla  Lee
    I got 100% on the math lesson that my teacher gave me before.
    (8 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Ojal Shandil
    can someone explain the whole simplifying the fractions bit, im so confused
    (3 votes)
    Default Khan Academy avatar avatar for user
  • starky ultimate style avatar for user Ryan
    Any reason to not write 150% as a mixed number? 1 1/2?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • winston default style avatar for user Daniel Ropalidis
    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)
    Default Khan Academy avatar avatar for user
    • cacteye blue style avatar for user Jerry Nilsson
      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)
  • female robot grace style avatar for user Housholder Brynna
    I Don't understand any of this! D: SOMEONE EXPLAIN IT PLEASE!!
    (2 votes)
    Default Khan Academy avatar avatar for user
  • spunky sam blue style avatar for user Samir Gunic
    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)
    Default Khan Academy avatar avatar for user
  • starky tree style avatar for user marqimoth
    how do you know what 150% means, 150% of what?
    (1 vote)
    Default Khan Academy avatar avatar for user

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.