user
How to simplify a divided by b the whole divided by c ?
alphonsio

$(a/b)/c$ simplifies to $\frac{a}{bc}$ :

$\frac{\frac{a}{b}}{c} = \frac{a}{b} \times \frac{1}{c} = \frac{a}{b \times c}$

To understand the formula $(a/b)/c$, let's break it down into its components and how to simplify it:

1. Start with the inner division: $a/b$.

• This means you are dividing $a$ by $b$.
2. Then, divide the result by $c$.

• This means you take the result of $a/b$ and divide it by $c$.

Mathematically, $(a/b)/c$ can be written as:

$\frac{\frac{a}{b}}{c}$

This expression can be simplified further. Division by a number is the same as multiplying by its reciprocal. Thus:

$\frac{\frac{a}{b}}{c} = \frac{a}{b} \times \frac{1}{c} = \frac{a}{b \times c}$

So, $(a/b)/c$ simplifies to $\frac{a}{bc}$.

### Example Calculation

Suppose $a = 10$, $b = 2$, and $c = 5$ .

1. Calculate $a/b$:

$\frac{10}{2} = 5$

2. Then divide by $c$:

$\frac{5}{5} = 1$

Using the simplified formula:

$\frac{a}{bc} = \frac{10}{2 \times 5} = \frac{10}{10} = 1$

Both methods yield the same result, confirming the simplification is correct.