Which is the sum of 8 ¾ + 2 ½?  A.  11 1/6  B. 11 ¼  C. 10 ½  D. 10 ¼  

Emily uses 1 2/3 cups of sugar and 3 ¼ cups flour to make muffins. She says she has 1 2/3 more cups of flour than sugar. Do you agree? Explain.   A. Yes; 3 ¼ - 1 2/3 = 1 2/3    B. No, the difference between 3 ¼ and 1 2/3 is 1 1/2 , not 1 2/3.   C. No, the difference between 3 ¼ and 1 2/3 is 1 7/12, not 1 2/3.   D. No; the sum of 3 ¼ and  1 /2/3 is 4 11/12, not 1 2/3.

Let's tackle each question step-by-step.

### First question: **What is the sum of 8 ¾ + 2 ½?**
1. **Convert to improper fractions:**
   - 8 ¾ = \( \frac{35}{4} \)
   - 2 ½ = \( \frac{5}{2} \)

2. **Find a common denominator:**  
   The least common denominator between 4 and 2 is 4.
   - \( \frac{5}{2} = \frac{10}{4} \)

3. **Add the fractions:**
   \[
   \frac{35}{4} + \frac{10}{4} = \frac{45}{4}
   \]

4. **Convert back to a mixed number:**
   \[
   \frac{45}{4} = 11 \frac{1}{4}
   \]

So, the sum is **11 ¼**, which matches **Option B**.

---

### Second question: **Emily uses 1 2/3 cups of sugar and 3 ¼ cups of flour to make muffins. She says she has 1 2/3 more cups of flour than sugar. Do you agree?**
1. **Find the difference between 3 ¼ cups of flour and 1 2/3 cups of sugar:**
   - 3 ¼ = \( \frac{13}{4} \)
   - 1 2/3 = \( \frac{5}{3} \)

2. **Find the common denominator (LCM of 4 and 3 is 12):**
   - \( \frac{13}{4} = \frac{39}{12} \)
   - \( \frac{5}{3} = \frac{20}{12} \)

3. **Subtract the fractions:**
   \[
   \frac{39}{12} - \frac{20}{12} = \frac{19}{12}
   \]

4. **Convert to a mixed number:**
   \[
   \frac{19}{12} = 1 \frac{7}{12}
   \]

So, the difference is **1 7/12**, not 1 2/3. Therefore, Emily is incorrect.

The correct answer is **Option C: No, the difference between 3 ¼ and 1 2/3 is 1 7/12, not 1 2/3.**

---

### Summary of answers:
1. The sum of 8 ¾ + 2 ½ is **11 ¼**, so the answer is **B**.
2. The difference between 3 ¼ cups of flour and 1 2/3 cups of sugar is 1 7/12, so the correct answer is **C**.

---

Would you like more details on any of these steps? Here are some related questions for practice:

1. What is the sum of 5 ½ and 3 ¼?
2. Subtract 4 2/3 from 7 1/2. What is the result?
3. How do you convert a mixed number to an improper fraction?
4. What is the least common denominator of 2/5 and 3/8?
5. Can you explain how to add fractions with different denominators?

**Tip:** When adding or subtracting fractions, always find a common denominator first. It makes the operation much easier!

Which is the sum of 8 ¾ + 2 ½? A. 11 1/6 B. 11 ¼ C. 10 ½ D. 10 ¼ Emily uses 1 2/3 cups of sugar and 3 ¼ cups flour to make muffins. She says she has 1 2/3 more cups of flour than sugar. Do you agree? Explain. A. Yes; 3 ¼ - 1 2/3 = 1 2/3 B. No, the difference between 3 ¼ and 1 2/3 is 1 1/2 , not 1 2/3. C. No, the difference between 3 ¼ and 1 2/3 is 1 7/12, not 1 2/3. D. No; the sum of 3 ¼ and 1 /2/3 is 4 11/12, not 1 2/3.

Solve the problem involving the addition of mixed numbers and subtraction of fractions. Learn how to add 8 ¾ and 2 ½, and evaluate whether the claim about the difference between 3 ¼ cups of flour and 1 2/3 cups of sugar is correct. This problem covers key concepts of improper fractions, common denominators, and fraction subtraction. Suitable for students in Grades 5-7.

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