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## Pre-algebra

### Course: Pre-algebra > Unit 7

Lesson 4: One-step multiplication and division equations- One-step division equations
- One-step multiplication equations
- One-step multiplication & division equations
- One-step multiplication & division equations
- One-step multiplication & division equations: fractions & decimals
- One-step multiplication equations: fractional coefficients
- One-step multiplication & division equations: fractions & decimals

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# One-step multiplication equations

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.

## Want to join the conversation?

- Do you multiply the denominator of the fraction by the fraction itself?(21 votes)
- 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!(20 votes)

- 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! :)(7 votes)
- All you usually have to do for multiplying is divide the number with the answer(9 votes)

- How is 42/3 = 14?(7 votes)
- Because if you divide 3 by 42, you get 14 lol(3 votes)

- Can anyone fully explain this to me to make it easier?(2 votes)
- 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.(15 votes)

- Why I am not able to rewatch this video? The replay button is not working?!(6 votes)
- Try closing down the browser and try again. If that doesn't work, use the Help Center link at the bottom of all KahnAcademy screens to get technical support.(7 votes)

- What am I learning ... Is this even math sometimes I just can't take this : ((9 votes)
- Why do i have to do math?!(6 votes)
- Because you need it in almost every job(3 votes)

- Why do you multiply the fraction to isolate the variable? Why can't you divide?(5 votes)
- 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(1 vote)

- How do you do this for decimals(6 votes)
- how does3 multiplyed by 3 get cancelled out(2 votes)
- 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.(6 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.