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# What Is a Reciprocal in Math?

**Reciprocals are two numbers that have one as their product when multiplied with each other.** They are most often expressed as proper or improper fractions.

To find the reciprocal of a given fraction, simply invert the fraction’s numerator and denominator. This means a fraction’s numerator becomes its reciprocal’s denominator, and its denominator becomes its reciprocal’s numerator. Obtain the reciprocal by flipping over the original number.

To get the reciprocal of a mixed number, first convert it into an improper fraction so the numerator and denominator can be interchanged. For example, to find the reciprocal of 3 ¼, rewrite it as 13/4. Then reverse the numerator and denominator to get the reciprocal, 4/13. Using reciprocals becomes necessary when one must rely on division to solve problems involving fractions.

For a word-problem example of real-world reciprocal use, suppose someone had 2 ¼ pizza left over after a party, was no longer hungry and wanted to invite some friends to finish it off, knowing each friend was capable of eating three-fourths of a pizza. Determining how many friends to invite is a matter of dividing 2 ¼ by three-fourths. When 2 ¼ is changed into an improper fraction, it becomes 9/4. To divided this by three-fourths, it must be multiplied times the reciprocal of three-fourths, which is four-thirds.

The product of 9/4 times four-thirds is 36/12. By dividing this fraction's numerator by its denominator, it becomes evident that the host can invite three friends over to finish the leftover pizza.

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