To calculate the total amount of ingredients that Emmanuel mixed together, we need to add the three amounts:
- Pancake mix: \( 2 \frac{3}{4} \) cups
- Water: \( 1 \frac{7}{8} \) cups
- Milk: \( \frac{2}{3} \) cups
First, we convert the mixed numbers into improper fractions:
- \( 2 \frac{3}{4} = \frac{11}{4} \)
- \( 1 \frac{7}{8} = \frac{15}{8} \)
Now, let's find a common denominator for the three fractions \( \frac{11}{4}, \frac{15}{8}, \) and \( \frac{2}{3} \).
The least common multiple (LCM) of the denominators \( 4, 8, \) and \( 3 \) is \( 24 \).
Now, convert each fraction to have a denominator of \( 24 \):
- \( \frac{11}{4} = \frac{11 \times 6}{4 \times 6} = \frac{66}{24} \)
- \( \frac{15}{8} = \frac{15 \times 3}{8 \times 3} = \frac{45}{24} \)
- \( \frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} \)
Now we can add these fractions together:
\[ \frac{66}{24} + \frac{45}{24} + \frac{16}{24} = \frac{66 + 45 + 16}{24} = \frac{127}{24} \]
Next, we convert \( \frac{127}{24} \) into a mixed number:
- Divide \( 127 \) by \( 24 \) to find how many whole numbers fit:
- \( 127 \div 24 \) is \( 5 \) with a remainder of \( 7 \).
Thus, \( \frac{127}{24} = 5 \frac{7}{24} \).
So the total amount of ingredients he mixed together is \( 5 \frac{7}{24} \).
The correct response is:
5 and 7 over 24