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How to Fix a Fraction With a Fraction in the Denominator

Dividing two fractions -- when there are fractions in both the numerator and the denominator -- looks far more difficult than it actually is. Multiplication and division are inverse operations; one is the reverse of the other. When you first learned how to divide numbers, you practiced facts such as, "If 3 times 2 equals 6, then 6 divided by 2 equals 3." If you turn these whole numbers into fractions, you'll see that all you have to do to solve the equation is invert the fraction in the denominator and multiply instead. Then you can apply this simple rule to more difficult problems.

Instructions

  1. Converting Whole Numbers to Fractions

    • 1

      Write the problem "6 divided by 2" as fractions instead of whole numbers. You can also write the number 6 as 6/1, and the number 2 as 2/1. Therefore, "6 divided by 2" is the same as "6/1 divided by 2/1."

    • 2

      Invert the fraction in the denominator so 2/1 becomes 1/2.

    • 3

      Perform the inverse operation. The inverse of division is multiplication. So after inverting the fraction 2/1 to 1/2, multiply the problem instead of dividing. The problem becomes 6/1 times 1/2.

    • 4

      Multiply the fractions by multiplying the numerators and then multiplying the denominators: 6 times 1 equals 6, and 1 times 2 equals 2. The answer is 6/2, or the whole number 3.

    Dividing Two Fractions

    • 5

      Recall the rule for dividing two fractions. To divide 4/5 by 2/3, invert the fraction in the denominator (2/3) so it becomes 3/2.

    • 6

      Multiply the two fractions by multiplying the numerators and then multiplying the denominators: 4/5 divided by 2/3 equals 4/5 multiplied by 3/2.

    • 7

      Multiply the numerators: 4 times 3 equals 12. Multiply the denominators: 5 times 2 equals 10. The answer is 12/10.

    • 8

      Reduce the fraction 12/10 to its lowest terms by finding a whole number other than 1 that you can divide into both the numerator and denominator. You can divide the number 2 evenly into both the numerator and the denominator: 12/2 equals 6, and 10/2 equals 5. So the answer is 6/5, which you can further reduce to 1 1/5.

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