To find the inverse (specifically, the multiplicative inverse), you determine the reciprocal of a number. The reciprocal, when multiplied by the original number, results in 1.
Here's how to find the multiplicative inverse:
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For Whole Numbers: The multiplicative inverse is simply 1 divided by the number. For example, according to the provided references:
- The multiplicative inverse of 9 is 1/9.
- The multiplicative inverse of -1/9 is -9.
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For Fractions: The multiplicative inverse is found by swapping the numerator and the denominator.
- If you have a fraction a/b, its multiplicative inverse is b/a.
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For Decimals: First, convert the decimal to a fraction. Then, find the reciprocal of that fraction. As shown in the provided reference:
- To find the multiplicative inverse of 0.9, convert it to 9/10. Then, the reciprocal (and therefore the multiplicative inverse) is 10/9.
Here's a summary in table form:
| Number | Multiplicative Inverse (Reciprocal) | Explanation |
|---|---|---|
| 9 | 1/9 | Reciprocal of the whole number. |
| -1/9 | -9 | Reciprocal of the negative fraction. |
| 0.9 | 10/9 | Decimal converted to fraction (9/10), then reciprocal found. |
It is important to remember that only multiplicative inverses are covered by this answer and the referenced material.
