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Lesson 3: One-step multiplication and division equations

# 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?
• 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
• How is 42/3 = 14?
• Because if you divide 3 by 42, you get 14 lol
• 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.
• What am I learning ... Is this even math sometimes I just can't take this : (
• 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
(1 vote)
• How do you do this for decimals
• 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.