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A rational number can be written in the form of a fraction, which is one integer divided by another integer. If you flip a fraction over, so that the top number (the numerator) turns into the bottom number (the denominator) and the bottom number becomes the top number, then that is called the reciprocal of that fraction (it can also be called the inversion of that fraction). So for example, two thirds is a rational number, 2/3; the reciprocal is 3/2.
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Is the reciprocal of every rational number possible?
No. 0 is rational and has no reciprocal.
What is the rational number that is equal to its reciprocal?
1
What types of numbers can you multiply together to get a rational number?
You can multiply any pair of rational numbers as well as any irrational number and its reciprocal (or a rational multiple of its reciprocal. Thus pi * 3/7*(1/pi) is rational.
Is the rational number -1 equal to its reciprocal?
Yes.
What pattern is there between a rational number and its reciprocal?
If the rational number is in the form of a proper or improper fraction, just exchange the numerator and the denominator. Thus, the reciprocal of 7/4 is 4/7.
