Question

to make soup, philip mixes 3 3/8
cups of broth with 2 1/4 cups of water. how many cups of liquid does he use? your answer should be written as a mixed number

Answer 1

To find the total amount of liquid Philip uses for his soup, we need to add the amounts of broth and water together:

1. **Convert mixed numbers to improper fractions**:
- For broth:
\[
3 \frac{3}{8} = 3 \cdot 8 + 3 = 24 + 3 = \frac{27}{8}
\]
- For water:
\[
2 \frac{1}{4} = 2 \cdot 4 + 1 = 8 + 1 = \frac{9}{4}
\]

2. **Find a common denominator** for the fractions. The denominators are 8 and 4. The least common multiple (LCM) is 8.

3. **Convert the water to have the same denominator**:
\[
\frac{9}{4} = \frac{9 \cdot 2}{4 \cdot 2} = \frac{18}{8}
\]

4. **Add the two fractions**:
\[
\frac{27}{8} + \frac{18}{8} = \frac{27 + 18}{8} = \frac{45}{8}
\]

5. **Convert the improper fraction back to a mixed number**:
- Divide 45 by 8: \(45 \div 8 = 5\) remainder \(5\).
- So, \( \frac{45}{8} = 5 \frac{5}{8} \).

Therefore, the total amount of liquid that Philip uses is \( \boxed{5 \frac{5}{8}} \) cups.