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Cross multiplication is a method used to solve proportions, which are equations that set two ratios equal to each other. Consider the proportion \( \frac{a}{b} = \frac{c}{d} \). Cross multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio and vice versa.

In the provided exercise, the proportions are set up as \( \frac{2.5}{0.6} = \frac{165}{n} \). To cross multiply, we multiply 2.5 by n and 165 by 0.6, creating the equation \( 2.5 \cdot n = 165 \cdot 0.6 \). This technique transforms the proportion into a regular equation and paves the way to find the unknown element 'n'.

Equations are foundational elements in prealgebra that express the equality between two expressions. When solving equations, the goal is to find the value of the unknown that makes the equation true.

The process involves using 'inverse operations' to isolate the variable. An inverse operation reverses the effect of the mathematical operation applied to a variable. For example, if a number is multiplied by 3, dividing it by 3 will undo the multiplication. The same principle is applied to solve for 'n' in our problem, leading us to the next step: isolating the variable.

In math, particularly when working with real-world data, specific levels of precision are often necessary. Rounding is the process of adjusting a number to a nearby value to make it simpler but still close to the original number. It can involve rounding to the nearest whole number, tenth, hundredth, and so on.

The exercise specifies rounding to the nearest hundredth, which requires us to look at the third decimal place. If the third decimal place is 5 or higher, we round up the second decimal place by one. For anything less than 5, we keep the second decimal place as is. After solving for 'n', the resulting value will be rounded to the nearest hundredth to achieve the precision required by the problem.

Isolating the variable is a crucial step in solving equations. It involves moving all the terms containing the variable to one side of the equation, and all the constant terms to the opposite side.

In the context of our exercise, after cross multiplication, we obtain the equation \( 2.5*n = 165*0.6 \). To isolate 'n', we divide both sides of the equation by the coefficient of 'n', which is 2.5. This operation leaves 'n' alone on one side, thus \( n = \frac{165*0.6}{2.5} \). Simplification of the right side then provides the value for 'n' that we can round to the nearest hundredth as the last step.