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One-step multiplication equations

Remember that what you do to one side, you have to do to the other. Will you multiply or divide both sides to dump the fraction, x/a? Let's do it together. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • blobby green style avatar for user kulshimako
    Do you multiply the denominator of the fraction by the fraction itself?
    (14 votes)
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    • aqualine ultimate style avatar for user ScienceLover7
      No, you don't multiply the denominator by the fraction. It would not simplify anything. For example :
      x/3 = 14
      (x*x/3)/(3*x/3) = 14[Since you have to keep the fraction the same, you have to multiply both the numerator and denominator]
      {(x^2)/3}/x Which is the same as x/3.
      What you have to do is multiply the entire fraction(not numerator and denominator separately) by the denominator. And, to maintain equality, do it on both sides. For example :
      x/5 = 200
      (x/5)*5 = 200*5
      The two 5s cancel.
      x = 1000
      Hope this helps!
      (11 votes)
  • blobby blue style avatar for user Terri
    I don't get why you would have to multiply or divide the fraction with X (or any other symbol/letter). Where did that rule come from? Please help! :)
    (4 votes)
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  • piceratops seed style avatar for user 550004035
    How do you do this for decimals
    (6 votes)
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  • starky sapling style avatar for user topher
    Why do i have to do math?!
    (4 votes)
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  • aqualine sapling style avatar for user gray battle
    i have a problem with: what is 7= 5/6c - 8, if c was the variable and 5/6 as a fraction?
    (4 votes)
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  • marcimus pink style avatar for user Darian Owens
    I really like this video. It helped me alot with my school work. But you didnt do an answer to something like 26=x/3 I was stuck on that one. Can you help?
    (3 votes)
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  • primosaur sapling style avatar for user mau
    Why do you multiply the fraction to isolate the variable? Why can't you divide?
    (2 votes)
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    • duskpin ultimate style avatar for user Dominic Nguyen
      Because, it would be like dividing x twice. To give a simple example for more understanding x-5=10, what you're thinking of is to subtract 5 from both sides, but that doesn't isolate x. In the same way, x/5=10, dividing by 5 wouldn't isolate the variable because it would become x/25=2. The only way that I can think of diving in an equation like x/5=10, would be to divide by 0.2, but dividing something by 0.2 would be the same as multiplying by 5. So basically, to isolate x, use the opposite operation. (subtraction,addition) (multiplication,division) and if you got to this (exponent, log) Hope this helps
      (4 votes)
  • primosaur sapling style avatar for user mau
    This was one of the questions correlated to this video: 10 / 3 = x / (-5/2); and I do not know how to solve it


    (2 votes)
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  • aqualine ultimate style avatar for user Sofia Cardozo
    Can anyone fully explain this to me to make it easier?
    (2 votes)
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    • aqualine ultimate style avatar for user Johnathan
      So say you have an equation like x/3 = 14. You want to know what x is. To do that, you have to use the different operations to isolate x. The number 3 is attached to x through division. We need to use the inverse operation to get x alone. If you do something to one side, we do it to the other side as well to balance out the equation. The inverse of addition is subtraction so the inverse of multiplication is division. So we'll multiply 3 to take out the divide 3. If the 3 was a 4, we would have used multiply 4 but this is a 3 so we'll multiply 3.
      x/3 * 3 = 14 * 3
      The 3's on the left hand side cancel out.
      x = 42. Tada...
      Hope this helps.
      (2 votes)
  • leafers tree style avatar for user Alfred Byrd
    so this is a question Ive had from an earlier video a cube Is any 3 deminsional shape that has 6 square sides on it yes or no
    (2 votes)
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Video transcript

Solve for x and check your solution. We have x divided by 3 is equal to 14. So to solve for x, to figure out what the variable x must be equal to, we really just have to isolate it on the left-hand side of this equation. It's already sitting there. We have x divided by 3 is equal to 14. We could also write this as 1/3 x is equal to 14. Obviously, x times 1/3 is going to be x/3. These are equivalent. So how can we just end up with an x on the left-hand side of either of these equations? These are really the same thing. Or another way, how can we just have a 1 in front of the x, a 1x, which is really just saying x over here? Well, I'm dividing it by 3 right now. So if I were to multiply both sides of this equation by 3, that would isolate the x. And the reason that would work is if I multiply this by 3 over here, I'm multiplying by 3 and dividing by 3. That's equivalent. That's equivalent to multiplying or dividing by 1. These guys cancel out. Remember, if you do it to the left-hand side, you also have to do it to the right-hand side. And actually, I'll do both of these equations at the same time, because they're really the exact same equation. So what are we going to get over here on the left-hand side? 3 times anything divided by 3 is going to be that anything. We're just going to have an x left over on the left-hand side. And on the right-hand side, what's 14 times 3? 3 times 10 is 30, 3 times 4 is 12. So it's going to be 42. So we get x is equal to 42. And the same thing would happen here. 3 times 1/3 is just 1. So you get 1x is equal to 14 times 3, which is 42. Now let's just check our answer. Let's substitute 42 into our original equation. So we have 42 in place for x over 3 is equal to 14. So what's 42 divided by 3? And we could do a little bit of-- I guess we call it medium-long division. It's not really long division. 3 into 4. 3 goes into 4 one time. 1 times 3 is 3. You subtract. 4 minus 3 is 1. Bring down the 2. 3 goes into 12 four times. 3 goes into 42 14 times. So this right over here simplifies to 14. And it all checks out, so we're done.