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.

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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.

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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.

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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!