Let's solve the given problem step-by-step.
### Adding the Fractions:
The question involves adding the fractions [tex]\( \frac{1}{3} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex].
#### Step 1: Finding a Common Denominator
To add two fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
#### Step 2: Converting the Fractions
Next, we convert each fraction to an equivalent fraction with the common denominator of 12:
1. For [tex]\( \frac{1}{3} \)[/tex]:
[tex]\( \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \)[/tex]
2. For [tex]\( \frac{1}{4} \)[/tex]:
[tex]\( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)[/tex]
#### Step 3: Adding the Fractions
Now we can add the fractions:
[tex]\[ \frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12} \][/tex]
Given this detailed breakdown, Shari's next step is:
[tex]\[ \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \][/tex]
So, the correct choice is:
[tex]\[ 4 / 12 + 3 / 12 = 7 / 12 \][/tex]
