A reciprocal is the multiplicative inverse of a number.

That means: two numbers are reciprocals if their product is 1.

Quick Scoop: What is a Reciprocal?

  • For any nonzero number aaa, its reciprocal is 1/a1/a1/a.
  • If you start with a fraction pq\frac{p}{q}qp​, its reciprocal is qp\frac{q}{p}pq​ (just flip numerator and denominator).
  • Example: the reciprocal of 5 is 1/51/51/5, and the reciprocal of 23\frac{2}{3}32​ is 32\frac{3}{2}23​.
  • A number and its reciprocal always multiply to 1 (like 5×15=15\times \frac{1}{5}=15×51​=1).
  • 0 does not have a reciprocal, because no number multiplied by 0 can give 1.

Tiny Story Example

Imagine you have a “do‑undo” button in math:

  • Multiplying by 4 “does” something to a number.
  • Multiplying by the reciprocal, 14\frac{1}{4}41​, “undoes” it and brings you back.

That “undo” partner is what we call the reciprocal.

TL;DR: A reciprocal is the number you multiply by to get 1; for a≠0a\neq 0a=0, the reciprocal is 1/a1/a1/a.

Information gathered from public forums or data available on the internet and portrayed here.