Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm learning Algebra and am curious about some methodological fundamentals here. One, in particular is why the following equation:

6(2x + 1 / 3) = 6(x + 4 / 2)

results in:

2(2x + 1) = 3(x + 4)

It's obvious that the distributive property swaps the numerators of the fractions and chooses to use another distributive property to complete the equation. Is there a specific formula for this, and why does it work that way specifically?

share|cite|improve this question
Maybe you are mistyping $6(2x+1/3)$ instead of $6((2x+1)/3)$? Perhaps what the author wrote is $6\frac{2x+1}{3} = 6\frac{x+4}{2}$? – Dilip Sarwate Oct 7 '11 at 18:31
What you wrote is correct if you have $6((2x+1)/3) = 6((x+4)/2)$. But $2x+1/3$ is not the same as $(2x+1)/3)$ and $x+4/2$ is not the same as $(x+4)/2$. – Michael Hardy Oct 7 '11 at 19:14

HINT $\ $ Apply the associative law $\rm\displaystyle\ \ A\ \bigg(\!\frac{1}{B}\ C\bigg)\ =\ \bigg(A\ \frac{1}B\bigg)\ C$

share|cite|improve this answer
Also @lhf Taken as typed by the OP, $6(2x + 1/3)$ works out to $12x + 2$, not $2(2x + 2)$ which is what $6((2x + 1)/3)$ works out to be. I believe that the OP is confused by his own mis-typing (and also possibly by how to apply the associative law to fractions..) – Dilip Sarwate Oct 7 '11 at 19:17
@Dil Surely the OP intends $\:(2\:x+1)/3\:,\:$ else the stated answer would be incorrect. – Bill Dubuque Oct 7 '11 at 20:21

$$a \left(\frac b c\right) = \frac a1 \frac b c = \frac {ab}{1c} = \frac {ab}{c1} = \frac ac \frac b1 = \frac ac b$$

share|cite|improve this answer

May be the following steps help you see how you get the result from the given expression - Swapping is fine as long as you understand the meaning of it so that you don't make mistakes.


$6 \left ( \frac{2x+1}{3} \right )= 6 \left ( \frac{x+4}{2} \right )$

a-multiply both sides by 1/6 to get:

$ \left ( \frac{2x+1}{3} \right )= \left ( \frac{x+4}{2} \right )$

b-multiply both sides by 3 to get:

$ 3\left ( \frac{2x+1}{3} \right )= 3 \left ( \frac{x+4}{2} \right )$

c-This is equal to:

$ \left ( \frac{2x+1}{1} \right )= 3 \left ( \frac{x+4}{2} \right )$

d-Multiply both sides by 2

$2 \left ( \frac{2x+1}{1} \right )= 2 * 3 \left ( \frac{x+4}{2} \right )$

e-Simplifying the right hand side you get

$2 \left ( \frac{2x+1}{1} \right )= 3 \left ( \frac{x+4}{1} \right )$

f-Which is:


share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.