Question

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solve \\(\frac{1}{3} = \frac{t}{9}\\).
t = __

Explanation:

Step1: Identify the equation

We have the equation \(\frac{1}{3}t=\frac{1}{9}\). To solve for \(t\), we need to isolate \(t\).

Step2: Multiply both sides by 3

Multiply both sides of the equation by 3 to get rid of the fraction on the left side. Using the property of equality, if \(\frac{1}{3}t = \frac{1}{9}\), then \(3\times\frac{1}{3}t=3\times\frac{1}{9}\).
Simplifying the left side, \(3\times\frac{1}{3}t = t\).
Simplifying the right side, \(3\times\frac{1}{9}=\frac{3}{9}=\frac{1}{3}\)? Wait, no, wait. Wait, \(3\times\frac{1}{9}=\frac{3}{9}=\frac{1}{3}\)? Wait, no, let's do it again. Wait, the equation is \(\frac{1}{3}t=\frac{1}{9}\). To solve for \(t\), we can multiply both sides by the reciprocal of \(\frac{1}{3}\), which is 3. So \(t=\frac{1}{9}\times3\). \(\frac{1}{9}\times3=\frac{3}{9}=\frac{1}{3}\)? Wait, no, \(\frac{1}{9}\times3=\frac{3}{9}=\frac{1}{3}\)? Wait, no, 3 divided by 9 is \(\frac{1}{3}\)? Wait, no, 3/9 simplifies to 1/3? Wait, no, 3 divided by 9 is 1/3? Wait, yes, because 3 ÷ 9 = 1/3. Wait, but let's check. If \(t = \frac{1}{3}\), then \(\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}\), which matches the right side. Wait, no, wait: \(\frac{1}{3}t=\frac{1}{9}\). If \(t=\frac{1}{3}\), then \(\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}\), which is correct. Wait, but let's do the multiplication again. So, multiplying both sides by 3: \(t=\frac{1}{9}\times3=\frac{3}{9}=\frac{1}{3}\). Wait, but let's check with another method. Alternatively, we can divide both sides by \(\frac{1}{3}\), which is the same as multiplying by 3. So, \(t=\frac{1}{9}\div\frac{1}{3}=\frac{1}{9}\times3=\frac{1}{3}\).

Wait, but maybe I made a mistake. Wait, let's re-express the equation. \(\frac{1}{3}t=\frac{1}{9}\). To solve for \(t\), we can multiply both sides by 3. So, \(t = \frac{1}{9} \times 3\). 3 times 1 is 3, over 9, so \(\frac{3}{9}\), which simplifies to \(\frac{1}{3}\). So \(t=\frac{1}{3}\). Wait, but let's check. If \(t=\frac{1}{3}\), then \(\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}\), which is correct. So that's the solution.

Answer:

\(t = \frac{1}{3}\)