Definition: The reciprocal of a nonzero number is the number you multiply it by to get 1, found by flipping a fraction upside down.
What is a reciprocal?
Two numbers are reciprocals when their product is 1. The reciprocal of 3/7 is 7/3, because 3/7 x 7/3 = 21/21 = 1.
How do you find one?
Swap the numerator and denominator. For a whole number, write it as a fraction first: 5 is 5/1, so its reciprocal is 1/5. For a mixed number, convert to an improper fraction: 2 1/4 = 9/4, whose reciprocal is 4/9.
How does it help divide fractions?
Dividing by a fraction is the same as multiplying by its reciprocal. To find 6 divided by 3/4, compute 6 x 4/3 = 24/3 = 8. Mathbot has 6 yards of cable and cuts pieces 3/4 yard long, so he gets 8 pieces.
What is special about zero?
Zero has no reciprocal, because no number times 0 equals 1.
What is the common mix-up?
Confusing reciprocal with opposite. The reciprocal of 4 is 1/4, while the opposite of 4 is -4.