The multiplicative inverse of a number, when multiplied by the original number, equals 1. Here's how to find it:
Understanding Multiplicative Inverse
The multiplicative inverse, also known as the reciprocal, is a number which, when multiplied by the original number, results in 1.
Finding the Multiplicative Inverse
- For any non-zero number x, the multiplicative inverse is simply 1/x. According to the reference, if x is any natural number, its multiplicative inverse is 1/x.
Examples
Here are a few examples to illustrate how to find the multiplicative inverse:
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Example 1: Natural Numbers
- Original Number: 5
- Multiplicative Inverse: 1/5
- Verification: 5 * (1/5) = 1
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Example 2: Fractions
- Original Number: 2/3
- Multiplicative Inverse: 3/2 (Flip the fraction)
- Verification: (2/3) * (3/2) = 1
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Example 3: Integers
- Original Number: -4
- Multiplicative Inverse: -1/4
- Verification: -4 * (-1/4) = 1
Special Cases
- Zero (0): Zero does not have a multiplicative inverse because no number multiplied by zero will equal 1.
Summary Table
| Original Number (x) | Multiplicative Inverse | Verification |
|---|---|---|
| 5 | 1/5 | 5 * (1/5) = 1 |
| 2/3 | 3/2 | (2/3) * (3/2) = 1 |
| -4 | -1/4 | -4 * (-1/4) = 1 |
| 0 | Does not exist | No number multiplied by 0 equals 1 |
