91Ó°ÊÓ

Solving equations means finding the value of the variable that makes the equation true. In our exercise, we are given the equation \(\frac{a}{0.3} = -24\). To solve this equation, we need to isolate the variable \(a\). Here’s how to do it step by step:

1. First, understand what the equation represents. In this case, \(a\) divided by \(0.3\) equals \(-24\).
2. To isolate \(a\), we need to get rid of the division by \(0.3\). This can be achieved using the multiplication property.

Remember, the goal of solving an equation is to perform operations that will isolate the variable on one side of the equation.

The multiplication property of equality is a fundamental concept used in solving equations. It states that if you multiply both sides of an equation by the same nonzero number, the two sides remain equal.

In our exercise, we have \(\frac{a}{0.3} = -24\). To eliminate the fraction and isolate \(a\), you multiply both sides by \(0.3\):
\[\begin{equation} \[0.3 \times \frac{a}{0.3} = -24 \times 0.3\] \end{equation}\]

On the left side, \(0.3 \times \frac{a}{0.3}\) equals \(a\) because \(0.3\) and \( \frac{1}{0.3} \) cancel out. Therefore, the equation simplifies to:
\[\begin{equation} \[a = -24 \times 0.3\] \ \end{equation}\]

Multiplying both sides by \(0.3\) allows you to isolate \(a\) to find its value.

Dealing with fractions in equations can be tricky, but it’s essential to understand how to simplify them appropriately. When fractions appear in equations, you often multiply by the fraction's denominator to eliminate it. This is exactly what we did in our exercise.

Given \(\frac{a}{0.3} = -24\), we multiplied both sides by \(0.3\) to get:
\[0.3 \times \frac{a}{0.3} = -24 \times 0.3\]

This simplification works because multiplying by the denominator of the fraction cancels it out. After performing the multiplication, you get:
\[a = -24 \times 0.3\]

Then, calculate the product to find the value of the variable. In this instance:
-24 \(\times 0.3 = -7.2\). Therefore, \(a = -7.2\).Always remember, when fractions are involved in equations, multiplying through by the denominator simplifies the equation and helps isolate the variable.