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How to Solve Rational Equations by Using Cross Products

Rational equations deal with ratios, usually expressed as fractions. In a typical equation, two fractions with variables are set as equal to one another, often with different denominators. Since you can only compare fractions with like denominators, you could take the time to convert the divisor, but it is often faster to turn the division problem into a multiplication problem instead. Cross multiplication accomplishes this by multiplying the numerator of one fraction by the denominator of the other.

Instructions

    • 1

      Multiply the numerator of the first fraction by the denominator of the second. Write this number down on one side of the equals sign. For instance, to solve the equation:

      4/6 = x/9

      first multiply 4 and 9. Write this down as:

      36 =

    • 2

      Multiply the denominator of the first fraction by the numerator of the second. Write this number on the other side of the equals sign:

      6 * x = 6x

      Therefore, the equation becomes:

      36 = 6x.

    • 3

      Rearrange the equation algebraically to isolate the variable on one side. Often this will mean dividing by the variable's coefficient, but sometimes you may need to add or subtract as well. By dividing each side by 6, you get the solution:

      6 = x

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