Question

4 over 3x + 2 over 3 = 6

Answer 1

4/3x + 2/3 = 6 ?

Answer 2

So, the problem is 4 over 3x plus two-thirds equals 6? Just want to make sure I am reading it correctly.

Answer 3

yes that is correct

Answer 4

Ok, thanks! There is more than one way you could start on this. One way might be to combine the fractions on the left side of the equation.

Answer 5

But to do that, they'd have to have the same denominator.

Answer 6

So, if you wanted a common denominator for 4/3x and 2/3, what would your common denominator be?

Answer 7

Isnt the two 3s the common denominator already?

Answer 8

Close! Both denominators have 3 as a factor. :)
What you want is the least common multiple of 3 and 3x.

Answer 9

That would be 1 correct?

Answer 10

Actually, you want an expression that both 3 and 3x would divide into

Answer 11

which would be 3x.

Answer 12

When you said "3" what you gave was the greatest common factor (the largest thing that would divide into both 3 and 3x). We wanted the smallest expression that both 3 and 3x could divide into, which is 3x. Does that make sense?

Answer 13

If not, I will think of another way to word it. :)

Answer 14

Yes that does, Thank you!

Answer 15

Ok, good :) So 4/3x already has 3x as a denominator.
And we want to change 2/3 into an equivalent fraction that has 3x as a denominator also.

Answer 16

So, what can you multiply 2/3 by so that you have 3x in the denominator?

Answer 17

Instead of just 3.

Answer 18

Im sorry, i have no idea

Answer 19

That's ok. This is what I was getting at: You want both fractions to have the same denominator, so that you can add them together. In order to do that, you have to find a common denominator, which is the least common multiple of the denominators of the fractions you have. In this case, the denominators were 3 and 3x, and so the least common multiple - an expression that both 3 and 3x are factors of - is 3x. Since the 4/3x already has 3x as a denominator, we leave it alone. To change the 2/3 to an equivalent fraction that has 3x as a denominator, we can multiply 2/3 by x/x.

Answer 20

The reason we can multiply by x/x is because x/x = 1.

Answer 21

And when you multiply a number by 1, what do you get?

Answer 22

You get the same number you started out with, right? When you multiply 2/3 by 1, you still have 2/3.

Answer 23

So, since x/x = 1, when you multiply 2/3 by x/x, you get a fraction that still is the same amount as 2/3, but it just looks different: 2x/3x

Answer 24

2x/3x is equivalent to 2/3, but it has the denominator we want. Does that make sense?

Answer 25

Yes it does!

Answer 26

Ok, good! :D Sorry I am so wordy! ;)

Answer 27

So now we have 4/3x + 2x/3x = 6

Answer 28

And since the fractions have the same denominator, we can combine the sum into one fraction:

(4 + 2x)/3x = 6

Answer 29

Do you have an idea of what you would do next?

Answer 30

Not really, no.