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Let's solve this step-by-step by adding the quantities of the ingredients Connor mixed.

1. **Ingredients to mix**:
   - \( \frac{1}{4} \) cups of sugar
   - \( 2 \frac{2}{3} \) cups of flour (which is a mixed number, so we need to convert it to an improper fraction)
   - \( 1 \frac{1}{6} \) cups of nuts (another mixed number to be converted)

### Step 1: Convert mixed numbers to improper fractions
- \( 2 \frac{2}{3} \) = \( \frac{2 \times 3 + 2}{3} = \frac{8}{3} \) (for flour)
- \( 1 \frac{1}{6} \) = \( \frac{1 \times 6 + 1}{6} = \frac{7}{6} \) (for nuts)

Now, we are left with:
- \( \frac{1}{4} \) cups of sugar
- \( \frac{8}{3} \) cups of flour
- \( \frac{7}{6} \) cups of nuts

### Step 2: Find a common denominator
To add these fractions, we need a common denominator. The denominators are 4, 3, and 6. The least common denominator (LCD) of 4, 3, and 6 is 12.

- Convert \( \frac{1}{4} \) to a fraction with a denominator of 12: 
  \[
  \frac{1}{4} = \frac{3}{12}
  \]
- Convert \( \frac{8}{3} \) to a fraction with a denominator of 12: 
  \[
  \frac{8}{3} = \frac{32}{12}
  \]
- Convert \( \frac{7}{6} \) to a fraction with a denominator of 12: 
  \[
  \frac{7}{6} = \frac{14}{12}
  \]

### Step 3: Add the fractions
Now, we can add the fractions:
\[
\frac{3}{12} + \frac{32}{12} + \frac{14}{12} = \frac{3 + 32 + 14}{12} = \frac{49}{12}
\]

### Step 4: Convert to a mixed number
Convert \( \frac{49}{12} \) to a mixed number:
\[
49 \div 12 = 4 \text{ remainder } 1
\]
So, \( \frac{49}{12} = 4 \frac{1}{12} \).

### Conclusion
Connor mixed **4 \(\frac{1}{12}\)** cups of dry ingredients.

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the least common denominator of multiple fractions?
2. How do you convert improper fractions to mixed numbers?
3. What are some tips for adding fractions with different denominators?
4. Can you explain why mixed numbers must be converted to improper fractions before adding them?
5. How do you convert mixed numbers back to improper fractions for other operations?

**Tip**: When adding fractions, always look for the least common denominator to simplify the process.

Connor gathered dry ingredients to make a large pan of brownies. He mixed 1/4 cups of sugar, 2 2/3 cups of flour, and 1 1/6 cups of nuts. How many cups of dry ingredients did he mix? Show all your work.

Learn how to add mixed numbers and fractions by solving a real-life problem. Connor mixed 1/4 cups of sugar, 2 2/3 cups of flour, and 1 1/6 cups of nuts. This detailed solution explains improper fractions, finding the least common denominator, and converting mixed numbers. Suitable for students in Grades 5-7.

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