Clearing of Fractions - Solution / Question

[Guest]

In the following equation, the fractions are cleared by multiplying each term:

x/2 + x/3 + x/6 = 2

Multiplying each term by 2 x 3 x 6, the result is:

3 x 6x + 2 + 6x + 2 x 3x = 2 x 3 x 6 x 2

18x + 12x + 6x = 72

Dividing each term by 6:

3x + 2x + x = 12

6x = 12

x = 2


My question: Is there some steps missing ?

Also, in the problem, another solution is to multiply by the lcm (least common multiple) 6 and immediately get:

3x + 2x + x = 12

[Guest]

I would suggest to multiply by the least common multiple - 6, because you first multiply by 2 x 3 x 6 and then divide by 6.
And you could also point out that you divide the both sides by 6 at this step: 6x = 12

[Guest]

Thanks.

One question:

Why did they divide by 6 first instead of combing the like terms?

[Guest]

There is no difference but you are right I would combine the like terms and divide not by 6 and by 36 because you get
36x = 72
dividing the both sides by 36 you get
x = 2

[Guest]

Thanks.

[leesajohnson]

I don't think that any step is missing.

[Guest]

Ok, thanks.

[Guest]

In the following equation, the fractions are cleared by multiplying each term:

x/2 + x/3 + x/6 = 2

Multiplying each term by 2 x 3 x 6, the result is: .....What you are doing is multiplying each term by 2 x 3 x 6 = 36.

[3 x 6x + 2 + 6x + 2 x 3x = 2 x 3 x 6 x 2] .....I wouldn't do it this way as in this line. I would use 36 instead.


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I would multiply each term as it is:-

36 x (x/2) + 36 x (x/3) + 36 x (x/6) = 36 x (2) ....brackets not needed just to show each orig. term

18x + 12x + 6x = 72 .....you divided each by 6 here which is OK but I just collected the terms together

36x = 72

x = 2 ..........and I get the answer..............

You can see we didn't need to multiply each term by 2 x 3 x 6 = 36 because at the end we divided by 36.

We just needed to multiply by the lowest common multiple of the denominators of the fractions.

2 x 3 = 6, so 6 is 2 x 3 and 6 is 6 x 1 so 6 is a multiple of all the denominators so we just need to multiply each term by 6.
(36 was a multiple of each denominator but it wasn't the lowest.)

6 x (x/2) + 6 x (x/3) + 6 x (x/6) = 6 x (2)

3x + 2x + x = 12

6x = 12

x = 2

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[Guest]

x/2 + x/3 + x/6 = 2

Another way to do this type of question is to convert each term to the same common fraction in this case sixths because 1 half is 3 sixths, and 1 third is 2 sixths. Then put them over the common denominator of 6 and then multiply each side by 6. You should always try to use the lowest common denominator of the fractions as before.

3x/6 + 2x/6 + x/6 = 2

(3x + 2x + x)/6 = 2

now multiply both sides by 6

3x + 2x + x = 12

6x = 12

x = 2

[Guest]

Ok, thanks.