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Think of an equation as a balance scale. Whatever you do on one side, you have to do to the other side to keep it balanced. This means if you add, subtract, multiply, or divide something on one side, you need to do the same thing on the other side.

In the exercise, our starting equation is \(-\frac{t}{2} = 5\). Here, \(t\) is the unknown value that you want to find. Solving an equation means manipulating it to isolate \(t\) on one side. The ultimate goal is to find out what number \(t\) actually represents.

To isolate \(t\), start by eliminating the fraction, which we will cover in the next section. Once the fraction is cleared, you'll need to deal with any negative signs, which will be explained further in the section about negative numbers.

Fractions can make equations look more complex, but they can be managed easily with multiplication or division. The fraction \(-\frac{t}{2}\) in the equation represents \(\frac{t}{2}\) multiplied by \(-1\). The denominator, 2, indicates that \(t\) is being divided by 2.

To simplify and eliminate the fraction, multiply both sides of the equation by the denominator. This will "cancel out" the division and let you work with a simpler equation. So from \(-\frac{t}{2} = 5\), multiplying both sides by 2 gives us \(-t = 10\). Now, the equation doesn't contain a fraction anymore and is easier to solve.

Negative numbers can sometimes be tricky to handle, especially when solving equations. In the exercise, after eliminating the fraction, you are left with the equation \(-t = 10\). Here, \(t\) is multiplied by a negative sign.

The goal is to find \(t\), so we need to "flip" the negative back to positive. You can do this by multiplying or dividing both sides of the equation by \(-1\). This transforms \(-t = 10\) into \(t = -10\).

So, multiplying or dividing by \(-1\) changes the sign efficiently, solving for \(t\) as a positive value on the side you want it—a crucial step in getting the correct and final answer.