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

abc=ab×1c=ab×c\frac{\frac{a}{b}}{c} = \frac{a}{b} \times \frac{1}{c} = \frac{a}{b \times c}

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

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

    • This means you are dividing aa by bb.
  2. Then, divide the result by cc.

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

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


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

abc=ab×1c=ab×c\frac{\frac{a}{b}}{c} = \frac{a}{b} \times \frac{1}{c} = \frac{a}{b \times c}

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

Example Calculation

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

  1. Calculate a/ba/b:

    102=5\frac{10}{2} = 5

  2. Then divide by cc:

    55=1\frac{5}{5} = 1

Using the simplified formula:

abc=102×5=1010=1\frac{a}{bc} = \frac{10}{2 \times 5} = \frac{10}{10} = 1

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