$$\begin{gathered} Q. Simplify: \\ 9-3÷\frac{1}{3}+1. \end{gathered}$$
Clarify each step

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$$\begin{gathered} We apply the rule of BODMAS\hspace{0.17em}\left(Brackets-Of-Division-Multiplication-Addition-Subtraction\right) to answer the given question. \\ We have: 9 - 3 ÷ \frac{1}{3} + 1 \\ Here, we will first perform the operation of division. \\ So, 9 - 3 ÷ \frac{1}{3} + 1 \\ = 9 - 3 ÷ \frac{1}{3} + 1 \\ = 9 - 3 \times 3 + 1 \\ = 9 - 9 + 1 \\ Next, we will perform the operation of addition. \\ So, 9 - 9 + 1 = 9 - 8 \\ It is impor\tan t to note here that while adding, we add -9 + 1 = -8, and not 9 + 1 = 10 (See Note 1). \\ Finally, we will subtract. \\ So, 9 - 8 =\boxed{\mathbf{1}}, which is the final answer. \\ NOTE: 1) For any two numbers a and b, we can write a - b = a + \left(-b\right). So, we can write 9 - 9 + 1 = 9 + \left(-9\right) + 1 = 1. \end{gathered}$$

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