To solve the problem of adding the fractions [tex]\( \frac{1}{3} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex], let's follow a detailed step-by-step approach:
1. Find a common denominator for the fractions:
- The denominators of the fractions are 3 and 4.
- The least common multiple (LCM) of 3 and 4 is 12. This will be our common denominator.
2. Convert each fraction to have the common denominator:
- Convert [tex]\( \frac{1}{3} \)[/tex] to a fraction with denominator 12:
[tex]\[
\frac{1}{3} \times \frac{4}{4} = \frac{4}{12}
\][/tex]
- Convert [tex]\( \frac{1}{4} \)[/tex] to a fraction with denominator 12:
[tex]\[
\frac{1}{4} \times \frac{3}{3} = \frac{3}{12}
\][/tex]
3. Add the fractions with the common denominator:
- Now we add the numerators and keep the common denominator:
[tex]\[
\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}
\][/tex]
So, when adding [tex]\( \frac{1}{3} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex], the next step is to convert them to have a common denominator (12), add them together, and simplify the result if possible.
Therefore, Shari's next step should lead to:
[tex]\[
\frac{4}{12} + \frac{3}{12} = \frac{7}{12}
\][/tex]
Among the given options, the correct answer is:
[tex]\[
4 / 12 + 3 / 12 = 7 / 12
\][/tex]
