The problem involves adding two fractions to find the total amount of chocolate chips used by Samantha. Here’s a clear breakdown of the process and the solution:
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. 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 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 both fractions:
- \(\frac{3}{4}\) became \(\frac{15}{20}\).
- \(\frac{2}{5}\) became \(\frac{8}{20}\).
- We added the fractions to obtain \(\frac{23}{20}\).
- Finally, we expressed our answer in mixed number form as \(1 \frac{3}{20}\) cups or in improper fraction form as \(\frac{23}{20}\) cups.
Final Answer:
Samantha used a total of 1 \(\frac{3}{20}\) cups of chocolate chips or \(\frac{23}{20}\) cups of chocolate chips.
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