How to Divide a Fractional Algebraic Expression by a Fractional Algebraic Expression (Using the Fractional Bar Form)

Two Methods:Most Elementary SolutionSlightly Increased Complexity

Any middle school student and early high school student should be able to know how to multiply fractions. When it comes to dividing algebraic expressions in fraction bars (where both the numerator and denominator both contain fractions), it looks pretty tough. When you have no numbers involved, it gets even tougher. This article can explain how to solve this type of expression.

Method 1
Most Elementary Solution

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    Look at the problem. It'll look a bit weird to see it this way. But it'll all come naturally in the end.
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    Learn the basics of dividing fractions. You probably learned in middle school and some early high school courses, that you can keep the first number, change the operand to multiplication, and write the reciprocal of the other.
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Method 2
Slightly Increased Complexity

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    Look at the fraction directly on the problem page. You'll see that both sides of the fraction are two unique fractions.
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    Look for the numerator of the top fraction and the denominator of the bottom fraction (the "outside" expressions of the complex expression).
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    Multiply these two algebraic expressions.
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    Write your new fraction bar, once you've found your answer for the numerator of the solution fraction.
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    Multiply the remainder of the "inside" items.
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    Use this "remainder of inside" solution as the final solution's denominator.
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    Simplify your fraction to simplest form, if possible.

Tips

  • Sometimes, when either side has only one portion of the fraction, you'll have to "add in" a denominator of 1, as any number divided by that number/expression is that number/expression. This will be the case, when this portion is in the numerator of the complex expression or the denominator of the complex expression.
  • Always try to bring your answer to lowest form. If the numerator contains a portion of the denominator when factored, these two can be removed from both the numerator of the resultant as well as the denominator of the resultant answer.

Article Info

Categories: Algebra | Fractions