Sure! Let's work through this step-by-step.
The problem involves adding two fractions, [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex], and then reducing the final sum if possible.
### Step 1: Find the Least Common Multiple (LCM) of the Denominators
First, we need to determine the least common multiple (LCM) of the denominators of the fractions. The denominators are 4 and 12.
- The LCM of 4 and 12 is 12 (since 12 is the smallest number that both 4 and 12 divide into without a remainder).
### Step 2: Convert Fractions to Like Fractions
Next, we'll convert each fraction to an equivalent fraction with the common denominator of 12.
#### Convert [tex]\(\frac{1}{4}\)[/tex] to an equivalent fraction with denominator 12
To convert [tex]\(\frac{1}{4}\)[/tex] to a fraction with a denominator of 12, we multiply both the numerator and the denominator by the same number:
[tex]\[
\frac{1}{4} \times \frac{3}{3} = \frac{3}{12}
\][/tex]
#### Convert [tex]\(\frac{5}{12}\)[/tex] to an equivalent fraction with denominator 12
The fraction [tex]\(\frac{5}{12}\)[/tex] already has the denominator 12, so it remains unchanged:
[tex]\[
\frac{5}{12}
\][/tex]
### Step 3: Add the Like Fractions
Now we can add the fractions [tex]\(\frac{3}{12}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex]:
[tex]\[
\frac{3}{12} + \frac{5}{12} = \frac{3 + 5}{12} = \frac{8}{12}
\][/tex]
### Step 4: Reduce the Fraction (if possible)
Finally, we need to simplify [tex]\(\frac{8}{12}\)[/tex]. We do this by dividing the numerator and denominator by their greatest common divisor (GCD). The GCD of 8 and 12 is 4.
[tex]\[
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
\][/tex]
### Result
So, the solution to the problem is:
- The equivalent like fractions are [tex]\(\frac{3}{12}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex].
- The sum of the fractions is [tex]\(\frac{8}{12}\)[/tex], which simplifies to [tex]\(\frac{2}{3}\)[/tex].
Therefore, the final answer is:
[tex]\[
\boxed{\frac{2}{3}}
\][/tex]
