Question

Evaluate the expression for the given value of the variable. $$\frac{1}{12}+x \text { when } x=\frac{1}{6}$$

Short answer

The expression evaluates to \( \frac{1}{4} \) when \( x = \frac{1}{6} \).

Step-by-step solution

Understand the Problem

The problem is asking to evaluate a mathematical expression when the variable 'x' is equal to \( \frac{1}{6}\). So, first retrieve the mathematical expression, which is \( \frac{1}{12} + x \), and the value of 'x', which is \( \frac{1}{6} \).

Substitute the value of 'x'

Next, substitute the value of 'x' which is \( \frac{1}{6} \) into the given equation: \( \frac{1}{12} + \frac{1}{6} \).

Simplify

To add fractions, make sure the denominator is the same. As 12 and 6 are both divisible by 6, the first fraction remains as it is and multiply the numerator and denominator of second fraction by 2 to get the same denominator. The expression becomes \( \frac{1}{12} + \frac{2}{12} \).

Complete the Mathematical Operation

Now, adding the fractions which have the same denominators. Sum the numerators and keep the denominators the same, i.e., \( \frac{1+2}{12} \) which simplifies to \( \frac{3}{12} \)

Simplify the Result

Finally, simplifying the final fraction \( \frac{3}{12} \) by dividing both the numerator and the denominator by their greatest common divisor which is 3, the result becomes \( \frac{1}{4} \).