Let's break down the problem step by step.

Step 1: Total weight of flour Mrs. Phua bought

She bought 2 bags of flour, each weighing $2 \frac{1}{2}$ kg.

Convert $2 \frac{1}{2}$ into an improper fraction: $2 \frac{1}{2} = \frac{5}{2} \text{ kg}$

So, the total weight of flour is: $2 \times \frac{5}{2} = 5 \text{ kg}$

Step 2: Flour used to bake cakes

Mrs. Phua used $1 \frac{5}{6}$ kg of flour to bake cakes.

Step 3: Flour remaining after baking cakes

The remaining flour is: $5 - 1 \frac{5}{6} \text{ kg}$

Convert $1 \frac{5}{6}$ into an improper fraction: $1 \frac{5}{6} = \frac{11}{6} \text{ kg}$

So, the remaining flour is: $5 - \frac{11}{6} = \frac{30}{6} - \frac{11}{6} = \frac{19}{6} \text{ kg}$

Step 4: Flour used to bake cookies

She used $\frac{3}{4}$ of the remaining flour to bake cookies: $\text{Flour used for cookies} = \frac{3}{4} \times \frac{19}{6} = \frac{57}{24}$

Step 5: Simplify the fraction

$\frac{57}{24}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3: $\frac{57 \div 3}{24 \div 3} = \frac{19}{8}$

Thus, the amount of flour she used to bake the cookies is $\frac{19}{8}$ kg, which can also be written as $2 \frac{3}{8}$ kg.

Final Answer:

Mrs. Phua used $\frac{19}{8}$ kg, or $2 \frac{3}{8}$ kg of flour to bake the cookies.

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

1. How do you convert a mixed number to an improper fraction?
2. What is the greatest common divisor (GCD), and how is it used to simplify fractions?
3. How do you multiply fractions?
4. How can you convert an improper fraction back into a mixed number?
5. What are some examples of real-life situations where fractions are used?

Tip: Always simplify fractions at the final step to ensure your answer is in its simplest form.