Linear Algebra For Dummies
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You can use the reciprocal of the number that you’re trying to “get rid of” if a fraction is multiplying the variable. You solve linear equations with reciprocals when you see a fraction — it's easier than using multiplication or division.

Here is an example of a fraction multiplying the variable:

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Look at the following examples of reciprocals — after the reciprocals, you can see how each, when multiplied together, equals 1.

  • 5 and 1/5 are reciprocals:

    image1.png
  • −3/7 and −7/3 are reciprocals:

    image2.png

Solving equations in the fewest possible steps is usually preferable.

Example:

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Use the following steps to solve for the variable, using reciprocals.

  1. Multiply each side by the reciprocal.

    In this example, the variable is multiplied by 4/5. So each side of the equation needs to be multiplied by the reciprocal 5/4.

    image4.png
  2. Reduce and simplify.

    image5.png

    On the left side, the 5s and 4s cancel each other out, and on the right side, 12 divided by 4 equals 3, resulting in:

    a = 5 × 3

    a = 15

Decimals can be made into fractions, which are much easier to deal with and avoid the problem of inadvertently misplacing the decimal when performing operations.

About This Article

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About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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