Question

Samantha is baking cookies for a school fundraiser. She needs to mix different amounts of chocolate chips into her cookie dough. She first adds 3/4 cup of chocolate chips to the dough. Later, she decides to add an additional 2/5 cup of chocolate chips to make the cookies extra chocolatey. How many cups of chocolate chips does Samantha use in total for her cookie dough? HINT: When you need to combine mixed fractions for a total, you may need to change the denominators so that you can then work with the fractions. ***This is a multiple point question. To receive all of your points you will have to show ALL of your work. You will receive a score on this problem after your teacher grades it. 1 point for showing the equation you used to solve this problem. 1 point for showing the common denominator that you found to solve this problem. 1 point for writing the correct answer WITH label. 1 point for explaining/showing all of your work. 4 points total for this problem (4 points) 0 / 10000 Word Limit Skip to navigation

Answer 1

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.