To determine the total amount of chocolate chips Samantha used, we first need to add the two fractions representing the amounts of chocolate chips she added.
1. **Equation**:
The equation to find the total amount of chocolate chips Samantha used is:
\[ \frac{3}{4} + \frac{2}{5} \]
2. **Finding a Common Denominator**:
To add the fractions, we need to find a common denominator. The denominators are 4 and 5. The least common multiple (LCM) of 4 and 5 is 20.
So, we will convert each fraction to have a denominator of 20.
- For \(\frac{3}{4}\):
\[
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
\]
- For \(\frac{2}{5}\):
\[
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
\]
3. **Adding the Converted Fractions**:
Now we can add the two fractions:
\[
\frac{15}{20} + \frac{8}{20} = \frac{15 + 8}{20} = \frac{23}{20}
\]
4. **Writing the Correct Answer with Label**:
The total amount of chocolate chips Samantha used is:
\(\frac{23}{20}\) cups, or in a mixed number form, it is \(1 \frac{3}{20}\) cups of chocolate chips.
5. **Work Explanation**:
- We began with the initial amounts of chocolate chips: \(\frac{3}{4}\) and \(\frac{2}{5}\).
- We found a common denominator of 20.
- We converted the fractions to have the same denominator:
- \(\frac{3}{4}\) became \(\frac{15}{20}\).
- \(\frac{2}{5}\) became \(\frac{8}{20}\).
- Then we added the fractions in their new form to get \(\frac{23}{20}\).
- Finally, we expressed our final answer as "1 \(\frac{3}{20}\) cups" or simply \(\frac{23}{20}\) cups.
**Final Answer**:
Samantha used a total of **1 \(\frac{3}{20}\) cups of chocolate chips** or **\(\frac{23}{20}\) cups of chocolate chips**.