Reciprocal
The multiplicative inverse of a number.
Formula
Variables
Example
Reciprocal of 4 is 1/4
How it works
A reciprocal is the number that gives 1 when multiplied by the original number. For a nonzero number x, that partner is 1/x because x \u00d7 (1/x) = 1. This works only when x is not zero, since division by zero is undefined and no number can multiply by 0 to make 1.
When to use it
Use reciprocals when you need to "flip" a fraction, divide by a number by multiplying by its inverse, or simplify ratios and algebraic expressions. They also show up in unit conversions, rates, and formulas involving fractions or proportions.
Worked example, step by step
Find the reciprocal of 5/2. Step 1: Write the number as a fraction: 5/2 Step 2: Flip the numerator and denominator: 2/5 Step 3: Check: (5/2) \u00d7 (2/5) = 10/10 = 1 Final answer: the reciprocal of 5/2 is 2/5
Common mistakes to avoid
- Thinking the reciprocal of a number is its negative instead of its inverse
- Forgetting to flip both numerator and denominator for a fraction
- Trying to find the reciprocal of 0, which is not possible
Did You Know?
Every non-zero number has a reciprocal, but zero has none — dividing by zero has no meaningful answer.
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