The expression \((1a \times 2) \div (4a \times a \times b \times b)\) can be simplified step by step.

### Step 1: Simplify the Numerator and the Denominator
- The numerator is \(1a \times 2 = 2a\).
- The denominator is \(4a \times a \times b \times b = 4a^2b^2\).

### Step 2: Write the Fraction
The expression now becomes:
\[
\frac{2a}{4a^2b^2}
\]

### Step 3: Simplify the Fraction
- Simplify the constants: \( \frac{2}{4} = \frac{1}{2} \).
- Simplify the \(a\) terms: \( \frac{a}{a^2} = \frac{1}{a} \).

So, the expression simplifies to:
\[
\frac{1}{2ab^2}
\]

The final simplified expression is \(\frac{1}{2ab^2}\).

Would you like more details, or do you have any questions? 

Here are some related questions:
1. How would you simplify \(\frac{3a \times 2b}{6a^2 \times b^2}\)?
2. What happens if the numerator was \(3a^2 \times 4b\) instead?
3. How would you approach simplifying \(\frac{6x^3}{12x^2y^2}\)?
4. Can you explain how to handle negative exponents in similar expressions?
5. What changes in the simplification if \(b\) was a variable raised to a power \(n\) instead?

**Tip:** Always simplify the coefficients (numbers) and like terms (variables with the same base) separately when dealing with algebraic fractions.

Learn how to simplify the algebraic expression (1ax2) divided by (4xaxbxb) step-by-step with detailed explanations. This problem covers fraction simplification in algebra, focusing on constants and variable terms. Suitable for students in Grades 7-9.

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