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### Course: 6th grade (Illustrative Mathematics)>Unit 6

Lesson 4: Lesson 4: Practice solving equations and representing situations with equations

# 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.

## 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
• 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.
• Why do i have to do math?!
• Because you need it in almost every job
• How do you do this for decimals
• 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.
• why does math exist? i mean come on man i just wanna play minecraft... just why? my mother is having such high expectations for me. Ex.if i got a 70% she would disown me, please help.
• Why do you multiply the fraction to isolate the variable? Why can't you divide?
• 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