The reciprocal of a rational number is simply 1 divided by that number.
Here's how it works:
- Rational number: A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. Examples include 1/2, 3/4, and -5/7.
- Reciprocal: The reciprocal of a number is the number that, when multiplied by the original number, equals 1. In other words, it's the "opposite" of the original number in terms of multiplication.
- Finding the reciprocal: To find the reciprocal of a rational number, simply flip the fraction. For example, the reciprocal of 2/3 is 3/2, and the reciprocal of -5/7 is -7/5.
Example:
- The reciprocal of 5 (which can be written as 5/1) is 1/5.
Practical Insights:
- Reciprocals are used in various mathematical operations, including division and solving equations.
- Understanding reciprocals is important in fields like physics, engineering, and finance.
