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Prealgebra is the foundation for all higher levels of algebra. It introduces basic algebraic concepts such as variables, ratios, and proportions. Prealgebra helps you understand how to manipulate mathematical expressions and equations. This concept is essential because it lays the groundwork for understanding more complex algebraic problems later.

In prealgebra, you'll encounter terms like variables (letters representing numbers), constants (specific numbers), and coefficients (numbers multiplying variables). For example, in the equation \(\frac{h}{4}=-12\), h is the variable. The goal of prealgebra is often to solve for the variable, meaning finding out what number it represents. Understanding these basics prepares you for more advanced topics in algebra.

Isolating the variable means getting the variable (often represented by letters like x, y, or h) alone on one side of the equation. This is a crucial step in solving equations because it allows you to find the value of that variable.

In the equation \(\frac{h}{4}=-12\), our variable is h. To isolate h, we need to undo the division by 4. We do this by performing the opposite operation: multiplication.

To keep the equation balanced, we must perform this operation on both sides of the equation. By multiplying both sides by 4, the equation simplifies to:

\[\frac{h}{4} \times 4 = -12 \times 4 \]

This step gives us h alone on one side, so we can easily identify its value.

When solving equations, especially those involving fractions, multiplication is a powerful tool. It helps to clear fractions or coefficients attached to the variable. This operation simplifies the equation, making it easier to solve.

In our example, the original equation is \(\frac{h}{4}=-12\). To solve it, we multiply both sides by 4. Why 4? Because in the fraction \(\frac{h}{4}\), 4 is the denominator, and multiplying by it will cancel the division. So, our steps look like this:

\[\frac{h}{4} \times 4 = -12 \times 4 \]

This simplifies to
\(h = -48\).

Now, h is isolated and we see that h equals -48. Multiplying correctly ensures the equation stays balanced and gives us the correct value for the variable.