reciprocal

Everyday

1. Reciprocal means given and received in return; done by both people or sides for each other: "a reciprocal friendship". tree →
2. (maths) The reciprocal of a number is 1 divided by that number; a number times its reciprocal equals 1. tree →

In the lessons

In maths, reciprocals are used to divide fractions: to divide by a fraction, multiply by its reciprocal ("flip it"). In ethics and everyday life, «reciprocal» help or respect goes both ways. Phrases: «reciprocal of», «reciprocal arrangement», «reciprocal respect».

Examples

• The reciprocal of 4 is 1/4. tree →
• The reciprocal of 2/3 is 3/2. tree →
• To divide by 1/2, multiply by its reciprocal, 2. tree →
• Our schools have a reciprocal visit: we go to them, then they come to us. tree →
• Friendship should be reciprocal; both people care. tree →
• 5 × 1/5 = 1, so 1/5 is the reciprocal of 5. tree →
• The two countries have a reciprocal agreement on health care. tree →

Note

Adjective, and countable noun in maths. Pronounced ri-SIP-ro-kal. Maths: reciprocal of a/b is b/a; reciprocal of a whole number n is 1/n; zero has no reciprocal (you cannot divide by 0). A number and its reciprocal always multiply to 1. Do not confuse with «opposite» (the opposite of 5 is −5; they add to 0).