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Calculate the reciprocal (1/x) of any number. Get results in both decimal and fraction form, with automatic fraction simplification.
Enter a number or fraction (e.g., 5, 0.25, or 3/4)
Enter a number to calculate its reciprocal
Type any non-zero number. You can enter whole numbers, decimals, or fractions (using / notation).
Click the Calculate button or press Enter. The calculator will show the reciprocal in both decimal and fraction form.
View the step-by-step solution and verification to understand how the reciprocal was calculated.
Reciprocal of x = 1/x
The reciprocal is also called the multiplicative inverse.
1/(a/b) = b/a
Example: Reciprocal of 3/4 is 4/3
x × (1/x) = 1
A number times its reciprocal always equals 1
1/(1/x) = x
The reciprocal of a reciprocal is the original number
1/(ab) = (1/a) × (1/b)
Example: 1/(2×3) = (1/2) × (1/3) = 1/6
1/1 = 1, 1/(-1) = -1
1 and -1 are their own reciprocals
| Number | Reciprocal (Fraction) | Reciprocal (Decimal) |
|---|---|---|
| 2 | 1/2 | 0.5 |
| 3 | 1/3 | 0.333... |
| 4 | 1/4 | 0.25 |
| 5 | 1/5 | 0.2 |
| 1/2 | 2/1 = 2 | 2 |
| 1/3 | 3/1 = 3 | 3 |
| 2/3 | 3/2 | 1.5 |
| 3/4 | 4/3 | 1.333... |
| 0.5 | 2/1 = 2 | 2 |
| 0.25 | 4/1 = 4 | 4 |
A reciprocal of a number x is 1 divided by x, written as 1/x. It's also called the multiplicative inverse. When you multiply a number by its reciprocal, you always get 1. For example, the reciprocal of 5 is 1/5 = 0.2, and 5 × 0.2 = 1.
To find the reciprocal of a fraction, simply flip it (swap the numerator and denominator). For example, the reciprocal of 3/4 is 4/3. This works because 1 ÷ (3/4) = 1 × (4/3) = 4/3.
Zero has no reciprocal because the reciprocal would be 1/0, and division by zero is undefined in mathematics. There's no number that, when multiplied by 0, gives 1. This is a fundamental property of mathematics.
Only two numbers are their own reciprocals: 1 and -1. For 1: 1/1 = 1, and for -1: 1/(-1) = -1. These are the only numbers where x = 1/x.
The reciprocal is the multiplicative inverse (1/x), while the opposite is the additive inverse (-x). For example, the reciprocal of 5 is 1/5, but the opposite of 5 is -5. Reciprocals involve division, opposites involve subtraction.
Reciprocals are used in: electrical resistance calculations (parallel circuits), speed/time relationships (if you double speed, you halve time), cooking (recipe scaling), finance (converting rates), and physics (inverse relationships like gravity and distance).
Reciprocals represent one of the fundamental operations in mathematics: finding the multiplicative inverse. Just as subtraction is the inverse of addition, taking the reciprocal is the inverse of multiplication. This concept is essential in algebra, calculus, and many practical applications.
In everyday life, reciprocals appear in rate conversions (miles per hour ↔ hours per mile), resistance calculations in electronics, and scaling recipes. Understanding reciprocals helps you think about inverse relationships and solve division problems more intuitively.