Question

Can someone please explain how to solve this problem? 1/6+1/3=1/x . The answer is 2 , I just don't understand how to find it.

Answer 1

Try multiplying everything by 6(least common multiple of your denominators). That will clear the fractions.

Answer 2

Then you can cross-multiply the proportion if the solution isn't yet obvious.

Answer 3

I'm stuck after the first two fractions denominators cancel out.

Answer 4

I got 1+2=6/6x

Answer 5

There's no 6 in the denominator with the x.

Answer 6

why not? wasn't everything multiplied by 6? I'm so lost. Can you show me the work? maybe I'd understand it better.

Answer 7

Only multiply numerators.

Answer 8

but then how would the denominators cancel out?

Answer 9

\[( \frac{1}{6}+\frac{1}{3} =\frac{1}{x}) \cdot 6 \space \rightarrow \space 1+2=\frac{6}{x}.\]

Answer 10

The intermediate step looks like:
\[\frac{6}{6}+\frac{6}{3}=\frac{6}{x}.\]
The denominators cancel when you simplify the fractions.

Answer 11

Ohh I think I get it now.

Answer 12

An alternative way to do it is to simplify the left side first:
\[\frac{1}{6}+\frac{1}{3} \space \rightarrow \space \frac{3+6}{18} \space \rightarrow \space \frac{1}{2}.\]

Answer 13

Then with one-half = one-over-x, it should be obvious.

Answer 14

Generally, though, multiplying by the LCM of the denominators to clear fractions makes things much easier. In fact, the true LCM is actually 6x. If you multiplied everything by 6x, then it would have been very clear.

Answer 15

viz. x+2x=6.