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.