4.1 Fractions ‣ Chapter 4 Concrete algebra ‣ Part I A Level mathematics (and further mathematics) ‣ A calculus of the absurd‣ Chapter 4 Concrete algebra ‣ Part I A Level mathematics (and further mathematics) ‣ A calculus of the absurd

Fractions can be surprisingly confusing. For example, what is the value of the expression directly below (assuming $x\neq 0$ , as we can’t divide by $0$ )?

\frac{1}{\left(\frac{1}{x}\right)}

(4.1)

Here’s a reasonably good way to find the answer - multiply everything by $1$ .

$\displaystyle\frac{1}{\left(\frac{1}{x}\right)}$	$\displaystyle=\frac{1}{\left(\frac{1}{x}\right)}\times\frac{x}{x}$	(4.2)
	$\displaystyle=\frac{x}{\left(\frac{x}{x}\right)}$	(4.3)
	$\displaystyle=x$	(4.4)

We can then apply this principle to more complex fractions.

4.1 Fractions

4.1.1 Reciprocals of fractions