Answer

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**Hint:**We will first write the given expression in the fraction form and thus do the required modification on both the sides (LHS and RHS) and thus get the required answer.

**Complete step-by-step answer:**

Step by step answer:-

We are given that we need to solve $x \div 9 = 8$ and explain how we solved it.

Now, consider the given expression: $x \div 9 = 8$.

We can write this expression as following expression:-

$ \Rightarrow \dfrac{x}{9} = 8$

We will now just multiply both sides by 9 and get the following expression:-

$ \Rightarrow \dfrac{x}{9} \times 9 = 8 \times 9$

On the left hand side of the above expression, we will cut off 9 from both numerator and denominator in order to get the following expression:-

$ \Rightarrow x = 8 \times 9$

Now, we will just simplify the calculations on the right hand side by multiplying whatever is given in the above expression and thus we will get the following expression:-

$ \Rightarrow x = 72$

**Hence, the required answer is x = 72.**

**Note:**

The students must note that the modifications we did seem to be simple and are pretty simple but they actually use some theorems to be used in it.

Like when we multiplied the whole equation by 9, it was due to the fact that we know for sure that 9 is not equal to 0. Otherwise, if we multiply the equation by some variable like x or y or something, we need to be sure that it is never equal to 0.

Similar thing happened when we cancelled off 9 from numerator and denominator, we can never cancel a term if there is any chance of it being equal to 0. Here, we cancelled off 9 because we are very sure that it cannot be equal to 0.

These are small but very useful facts. While doing any question, always remember these kinds of things.

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