91Ó°ÊÓ

To solve an equation, we often need to find the value of the variable. In our given problem, the equation is \(\frac{2}{3} + t = 1\). Here, our goal is to isolate the variable \(t\). This means we want \(t\) to be alone on one side of the equation.

In many equations, isolating the variable involves using basic arithmetic operations. In this case, we subtract \( \frac{2}{3} \) from both sides of the equation. Why subtract? Because the opposite of adding \( \frac{2}{3} \) is subtracting it. This step will help us clear away the fraction on the left-hand side and our equation will look like this:

• \[ t = 1 - \frac{2}{3} \]

Now, \(t\) is isolated, and we can proceed with solving the expression on the right-hand side.

Subtracting fractions can sometimes be tricky. Let’s break it down to ensure you grasp it fully.

In our equation, we need to subtract \( \frac{2}{3} \) from \(1\). First, remember that the number \(1\) can be represented as a fraction. It can be written as \( \frac{3}{3} \), which makes subtraction straightforward. Keeping this in mind, we rewrite the equation:

• \[ t = \frac{3}{3} - \frac{2}{3} \]

Once you rewrite it in fraction form like this, subtracting fractions works by simply subtracting the numerators (the top numbers) while keeping the denominator (the bottom number) the same.

After rewriting the number \(1\) as a fraction and setting up \( t = \frac{3}{3} - \frac{2}{3} \), we move on to simplifying the fraction. This step is essential to finally solve for \(t\).

Here’s how you do it:

• First, subtract the numerators: \[ 3 - 2 = 1 \]
• Keep the common denominator: \[ \frac{1}{3} \]

With these steps, you arrive at the solution:

• \[ t = \frac{1}{3} \]

Simplifying fractions means making them as simple as possible, which often means reducing the numbers in the fraction to their smallest values.

Now that \( t = \frac{1}{3} \), you have successfully solved the equation by isolating the variable, subtracting fractions, and simplifying them!