Question

what number, when added to \\(\frac{1}{3}\\), gives the sum that is equal to the sum of \\(\frac{1}{4}\\) and \\(\frac{1}{6}\\) ?

Explanation:

Step1: Find sum of $\frac{1}{4}$ and $\frac{1}{6}$

First, find a common denominator for $\frac{1}{4}$ and $\frac{1}{6}$. The least common denominator of 4 and 6 is 12. Convert the fractions: $\frac{1}{4}=\frac{3}{12}$ and $\frac{1}{6}=\frac{2}{12}$. Then add them: $\frac{3}{12}+\frac{2}{12}=\frac{5}{12}$.

Step2: Let the number be $x$, set up equation

We know that $x + \frac{1}{3}=\frac{5}{12}$. To solve for $x$, subtract $\frac{1}{3}$ from both sides. Convert $\frac{1}{3}$ to twelfths: $\frac{1}{3}=\frac{4}{12}$. Then $x=\frac{5}{12}-\frac{4}{12}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$