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Let's analyze and solve the problem.

Dwayne needs:
- \( 1 \frac{2}{3} \) cups of cheese for the casserole
- \( \frac{3}{4} \) cups of cheese for the top

He has 3 cups of cheese in total, and we are asked to determine how much cheese he will have left.

### Step-by-step solution:

1. **Convert the mixed fraction** \( 1 \frac{2}{3} \) into an improper fraction:
   \[
   1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}
   \]

2. **Add the amounts of cheese he needs**:
   He needs \( \frac{5}{3} \) cups for the casserole and \( \frac{3}{4} \) cups for the top. We need to add these fractions:
   \[
   \frac{5}{3} + \frac{3}{4}
   \]
   To add fractions, we first find a common denominator. The least common denominator (LCD) of 3 and 4 is 12. So, we rewrite the fractions:
   \[
   \frac{5}{3} = \frac{20}{12}, \quad \frac{3}{4} = \frac{9}{12}
   \]
   Now, add the fractions:
   \[
   \frac{20}{12} + \frac{9}{12} = \frac{29}{12}
   \]

3. **Subtract the total cheese used from the amount he has**:
   Dwayne has 3 cups of cheese. To subtract the amount used \( \frac{29}{12} \) from 3, we convert 3 into a fraction with a denominator of 12:
   \[
   3 = \frac{36}{12}
   \]
   Now subtract:
   \[
   \frac{36}{12} - \frac{29}{12} = \frac{7}{12}
   \]

### Final answer:
Dwayne will have \( \frac{7}{12} \) cups of cheese left.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How do you convert a mixed fraction into an improper fraction?
2. What is the least common denominator (LCD) and why is it needed?
3. Can you solve a similar problem where different amounts of cheese are required?
4. How would the solution change if Dwayne had more or less than 3 cups of cheese?
5. What would happen if the total cheese required exceeds the amount available?

**Tip**: When adding or subtracting fractions, always find a common denominator first for easier calculation.

Dwayne needs 1 2/3 cups of shredded cheese to put in his enchilada casserole and 3/4 cup of cheese for the top. If he has 3 cups of cheese in all, how much cheese will he have left?

Solve a real-world math problem involving mixed fractions and subtraction. Dwayne needs 1 2/3 cups of cheese for his casserole and 3/4 cup for the top. Find out how much cheese he'll have left if he starts with 3 cups. Detailed step-by-step solution for students in Grades 6-8.

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