Do you multiply the denominator of the fraction by the fraction itself?

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!

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! :)

All you usually have to do for multiplying is divide the number with the answer

Because if you divide 3 by 42, you get 14 lol

Why do i have to do math?!

Because you need it in almost every job

Why do you multiply the fraction to isolate the variable? Why can't you divide?

Because, you are trying to solve the variable. That is why you isolate it. If it's not isolated, either the answer is not real or the answer is wrong. If that's the case, simplify the problem to the best that you can

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?

First, isolate x. We have x/3. To get x by itself, we must multiply the sides by 3, eliminating the fraction. 26=x/3 26(3)=x/3(3) 78=x x=78 No more simplifying to be done, so x=78.

Can anyone fully explain this to me to make it easier?

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.

how does3 multiplyed by 3 get cancelled out

The 3's that were written in are 3/1 in fraction form. 3/1 (x/3) = 3x/3 = x or 3/1 (1/3)x = (3/3)x = x Hope this helps.

Main content

Course: 6th grade (Eureka Math/EngageNY) > Unit 4

Lesson 6: Topic G: Solving equations

One-step multiplication equations

Name: One-step multiplication equations
Uploaded: 2011-02-20T16:40:20Z
Description: In this math lesson, we learn to solve equations with x divided by a number, like x/3 = 14. To find x, we isolate it by multiplying both sides of the equation by the divisor (3). This gives us x = 42. Finally, we check our answer by substituting x back into the original equation to make sure it's correct.

Google Classroom

In this math lesson, we learn to solve equations with x divided by a number, like x/3 = 14. To find x, we isolate it by multiplying both sides of the equation by the divisor (3). This gives us x = 42. Finally, we check our answer by substituting x back into the original equation to make sure it's correct. Created by Sal Khan and Monterey Institute for Technology and Education.

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kulshimako
Posted 8 years ago. Direct link to kulshimako's post “Do you multiply the denom...”
Do you multiply the denominator of the fraction by the fraction itself?
Button navigates to signup pageComment on kulshimako's post “Do you multiply the denom...”
(23 votes)
Answer
- ScienceLover7
  Posted 4 years ago. Direct link to ScienceLover7's post “No, you don't multiply th...”
  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!
  Comment on ScienceLover7's post “No, you don't multiply th...”
  (23 votes)
Terri
Posted 8 years ago. Direct link to Terri's post “I don't get why you would...”
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! :)
Button navigates to signup pageComment on Terri's post “I don't get why you would...”
(7 votes)
Answer
- fionaberhe04
  Posted 7 years ago. Direct link to fionaberhe04's post “All you usually have to d...”
  All you usually have to do for multiplying is divide the number with the answer
  Button navigates to signup page
  (9 votes)
Sofia Cardozo
Posted 8 years ago. Direct link to Sofia Cardozo's post “Can anyone fully explain ...”
Can anyone fully explain this to me to make it easier?
Button navigates to signup pageComment on Sofia Cardozo's post “Can anyone fully explain ...”
(2 votes)
Answer
- Johnathan
  Posted 8 years ago. Direct link to Johnathan's post “So say you have an equati...”
  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.
  Comment on Johnathan's post “So say you have an equati...”
  (15 votes)
AmariE
Posted a year ago. Direct link to AmariE's post “What am I learning ... Is...”
What am I learning ... Is this even math sometimes I just can't take this : (
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(9 votes)
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⚡🌠Iris East🌠⚡
Posted a year ago. Direct link to ⚡🌠Iris East🌠⚡'s post “How is 42/3 = 14?”
How is 42/3 = 14?
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(6 votes)
Answer
- ijohnson
  Posted 9 months ago. Direct link to ijohnson's post “Because if you divide 3 b...”
  Because if you divide 3 by 42, you get 14 lol
  Comment on ijohnson's post “Because if you divide 3 b...”
  (2 votes)
wewe
Posted 2 years ago. Direct link to wewe's post “Why do i have to do math?...”
Why do i have to do math?!
Button navigates to signup pageComment on wewe's post “Why do i have to do math?...”
(6 votes)
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- timothy.ogle0
  Posted a year ago. Direct link to timothy.ogle0's post “Because you need it in al...”
  Because you need it in almost every job
  Comment on timothy.ogle0's post “Because you need it in al...”
  (5 votes)
550004035
Posted 7 years ago. Direct link to 550004035's post “How do you do this for de...”
How do you do this for decimals
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(8 votes)
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derakeyy
Posted a year ago. Direct link to derakeyy's post “Why do you multiply the f...”
Why do you multiply the fraction to isolate the variable? Why can't you divide?
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(6 votes)
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- ijohnson
  Posted 9 months ago. Direct link to ijohnson's post “Because, you are trying t...”
  Because, you are trying to solve the variable. That is why you isolate it. If it's not isolated, either the answer is not real or the answer is wrong. If that's the case, simplify the problem to the best that you can
  Button navigates to signup page
  (2 votes)
Darian Owens
Posted 11 years ago. Direct link to Darian Owens's post “I really like this video....”
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?
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- The #3 Canvas Size Proponent/Fearless Runner(Joshua Chong)(Whitetail)
  Posted 10 years ago. Direct link to The #3 Canvas Size Proponent/Fearless Runner(Joshua Chong)(Whitetail)'s post “First, isolate x. We have...”
  First, isolate x. We have x/3. To get x by itself, we must multiply the sides by 3, eliminating the fraction.
  26=x/3
  26(3)=x/3(3)
  78=x
  x=78
  No more simplifying to be done, so x=78.
  Button navigates to signup page
  (5 votes)
noahfarooq78
Posted 9 months ago. Direct link to noahfarooq78's post “how does3 multiplyed by 3...”
how does3 multiplyed by 3 get cancelled out
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- Kim Seidel
  Posted 9 months ago. Direct link to Kim Seidel's post “The 3's that were written...”
  The 3's that were written in are 3/1 in fraction form. 3/1 (x/3) = 3x/3 = x or 3/1 (1/3)x = (3/3)x = x
  
  Hope this helps.
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  (7 votes)

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.