How to Do Reciprocals by Multiplying Fractions

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A reciprocal of a fraction is its inverse, meaning that the numerator (top value of the fraction) and the denominator (bottom number of the fraction) have changed places. When you are dividing fractions, you must insert a reciprocal and multiply to arrive at the correct answer. Multiplying fractions once you have inserted the reciprocal is a simple mathematical process. You might encounter these types of problems in math courses ranging from middle school to college.

  • Write down a division sentence containing fractions. For example, you might write down 4/5 / 1/2.

  • Flip the second fraction to form the reciprocal. In this example, you would flip 1/2 to create 2/1.

  • Multiply the numerators and denominators of the two fractions to find your answer. In this example, you would now have the sentence 4/5 x 2/1. You would multiply 4 and 2 to get 8 and 5 and 1 to get 5. Therefore, your answer would be 8/5.

  • Simplify your answer if possible. In this case, 8/5 is an improper fraction, meaning that the numerator is larger than the denominator. Therefore, you write down the number of times that the denominator will fit into the numerator, which in this case is 1. Write the remainder over the denominator. In this example, you would write 1 3/5. If your answer was a proper fraction that could be simplified, you would simply divide the numerator and denominator by the largest number that would fit into both values evenly.

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