Reciprocals (Cambridge International IGCSE Maths)

Reciprocals

What is a reciprocal?

• The reciprocal of a number is the result of dividing 1 by that number

  • Any number multiplied by its reciprocal will be equal to 1

• The reciprocal of 3 is $\frac{1}{3}$

  • The reciprocal of $\frac{1}{3}$ is 3
  • $3\times\frac{1}{3}=\frac{1}{3}\times3=1$

• The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$

  • The reciprocal of $\frac{3}{2}$ is $\frac{2}{3}$
  • $\frac{2}{3}\times\frac{3}{2}=\frac{3}{2}\times\frac{2}{3}=1$

• Algebraically the reciprocal of $a$ is $\frac{1}{a}$

  • The reciprocal of $\frac{1}{a}$ is $a$

  • This can also be written using a power of -1

    • $\frac{1}{a}=a^{-1}$

Worked Example Write down a fraction that completes this calculation: $\frac{3}{7}\times\frac{...}{...}=1$

Answer:

Recall that a number multiplied by its reciprocal is equal to 1

$\frac{3}{7}\times\frac{7}{3}=1$