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Understanding how to convert percentages to decimals is crucial for solving many math problems, including those on standardized tests like the ACT. Conversion is a simple process: divide the percentage by 100. The reason for dividing by 100 is that 'percent' literally means 'per hundred'. For example, if you have 40%, you divide 40 by 100, which gives you 0.4. This conversion allows you to work with numbers in equations more easily since percentage points are now transformed into a decimal that can be multiplied, divided, and used in algebraic equations seamlessly.

The process of converting a percentage to a decimal can be summarized in the following steps:

• Identify the percentage.
• Divide that number by 100.
• Use the resulting decimal in further calculations.

Algebraic equations are mathematical statements that show the relationship between different expressions. These equations are made up of variables (letters representing unknowns), coefficients (numbers multiplying the variables), and constants (numbers on their own). The goal when working with algebraic equations is often to solve for the unknown variable. This means manipulating the equation in a way that isolates the variable on one side, leaving a numerical value on the other.

For instance, in the equation from the ACT Math problem, \(18x = 0.4(180)\), \(0.4(180)\) is the expression obtained from converting a percentage to a decimal and multiplying it by a constant. The next step in solving the algebraic equation is to simplify and isolate the variable \(x\).

The general steps for solving algebraic equations are:

• Distribute any numbers outside parentheses.
• Combine like terms on each side of the equation.
• Isolate the variable using inverse operations (addition/subtraction, multiplication/division).

When it comes to solving for variables, the idea is to isolate the variable on one side of the equation. In the problem provided, once you have simplified \(18x = 0.4(180)\) to \(18x = 72\), the variable \(x\) is not yet isolated. To achieve this, you perform the inverse operation of multiplication, which is division in this case, by dividing both sides of the equation by 18, the coefficient of \(x\).

After dividing, the equation \(x = \frac{72}{18}\) simplifies to \(x = 4\), giving you the final answer for the variable. The ability to solve for variables is fundamental in algebra and tends to be involved in various applications ranging from simple calculations to more complex problem-solving situations.

Remember that consistent steps are key to variable isolation:

• Understand what operation is currently being applied to the variable.
• Apply the inverse operation to both sides of the equation.
• Simplify the expression to find the value of the variable.