I would like help in the explanation of this equation.

1/3x = 3 5/6

### 4 Answers | Add Yours

1/3 x = 3 5/6

First, change the mixed number to an improper fraction.

3 5/6 = 23/6

So now the equation is

1/3 x = 23/6

Multiply both sides of the equation by 3. This will cancel the 1/3 on the left side of the equation.

x = 69/6

Simplified:

x = 23/2

**Solution: x = 23/2 **or** x = 11.5**

We have to find x given that 1/3x = 3 5/6

3 5/6 is a mixed number with a whole number part 3 and a fraction 5/6. Convert it to an improper fraction 3 5/6 = (3*6 + 5)/6 = (18 + 5)/6 = 23/6

1/3x = 3 5/6

=> 1/3x = 23/6

=> 1/x = 23/2

=> x = 2/23

**The solution of the equation is x = 2/23**

ok, in this equation, there is a mixed fraction involved

3 5/6 literally means 3+(5/6)

adding them using the same base

It becomes (3*6+5)/6=23/6 which becomes an improper fraction

I actually have two interpretations of the equation

If it is 1/3 * x

Then The original equation turns out to be

1/3*x=23/6

multiply 3 to both sides

x=23/2

if the equation is 1/(3x)=3 5/6

then the original equation turns out to be

1/(3x)= 23/6

multiply 3 to both sides

1/x=23/2

using cross multiplication

1*2=23*X

divide by 23 on both sides

X= 2/23

**There seems to be a bit of confusion over whether your problem is (1/3)x = 3 5/6 or 1/(3x) = 3 5/6. The way you have it written appears more like the second option, but it seems more likely that it would be the first option. I will answer it as if it is (1/3)x = 3 5/6.**

(1/3)x = 3 5/6

First, change the mixed number to an improper fraction.

3 5/6 = 23/6

And change 1/3 x to x/3 since 1*x is x.

Now we have:

x/3 = 23/6

Cross products are equal when you have a proportion such as this.

So:

6x = (3)(23)

6x = 69

Divide both sides by 6.

x = 69/6

Reduce.

x = 23/2

This is equivalent to 11 1/2 since 23 divided by 2 is 11 remainder 1.

**So the answer is 11 1/2.**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes