If $$11m×11n=119 and $$m=2, what is the value of $$n?Enter each line of working as an equation.

1. Break Down the Problem

We need to find the value of $n$ given the equation $11m \times 11n = 119$ and the value of $m = 2$.

2. Relevant Concepts

We'll use the properties of multiplication and substitution to solve for $n$.

3. Analysis and Detail

1. Substitute the value of $m$ into the equation: $11(2) \times 11n = 119$
2. Simplify the left side: $22 \times 11n = 119$
3. Multiply the constants: $242n = 119$
4. Solve for $n$ by dividing both sides by 242: $n = \frac{119}{242}$

4. Verify and Summarize

Now, let's simplify the fraction: $n = \frac{119}{242} \text{ can be simplified since both components share a common factor of 11.}$ $n = \frac{119 \div 11}{242 \div 11} = \frac{11}{22} = \frac{1}{2}$

Final Answer

The value of $n$ is $\frac{1}{2}$.