What happens when you multiply a number by its reciprocal?

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The product of a number and its reciprocal is always one. To understand why, let’s break it down a bit.

A reciprocal of a number is simply what you get when you divide 1 by that number. For instance, if you take the number 5, its reciprocal would be 1/5. When you multiply these two together, you do the following calculation:

5 * (1/5) = 5/5 = 1

This principle holds true for any non-zero number. Let’s look at a couple more examples:

  • If you take the number 2, its reciprocal is 1/2. So, the product is:
    • 2 * (1/2) = 2/2 = 1
  • Now, consider the number 0.25. Its reciprocal is 4. Therefore, the calculation is:
    • 0.25 * 4 = 1

However, it’s important to note that the product of a number and its reciprocal is undefined when the number is zero, since the reciprocal of zero cannot be calculated.

In summary, regardless of the number you choose (as long as it’s not zero), multiplying it by its reciprocal will always yield a product of one. This concept is fundamental in mathematics and has applications in various fields, including algebra and calculus.

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