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A reciprocal is when you take the second fraction in a division problem and flip it Then change the sign to multiply. THIS ONLY WORKS WHEN YOU ARE DIVIDING FRACTIONS!
Division by a number is the same as multiplication by its reciprocal. That is, n / a = n * (1/a) and as you should know, (1/a) is the reciprocal of a.
Because multiplication and division are inverse operations. And the reciprocal of a number is its multiplicative inverse.
Division is multiply by the reciprocal.
To divide by a fraction, you multiply by its reciprocal. This is related to the facts that (1) division is the opposite of multiplication, and (2) a reciprocal is the multiplicative "opposite" of a number.