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Algebra I Recipe: Shortcuts for Solving Equations with Fractions and Decimals
A. Solving Equations with Fractions
  1. Multiply each term on both sides of the equation by the least common denominator. In some situations you may have to simplify the equation before multiplying by the LCD on both sides.
  2. Follow the same steps for solving equations as in Sec. 3.3.
  3. If the final answer is a fraction, it can be left as an improper fraction, just reduce completely.
  4. If the final answer is a fraction, it can be given in decimal form, but only if it is a stopping (terminating) decimal. Round only when you are asked to round.
In the following examples, leave your answer in fraction form if it is not an integer.
ExamplesExamples:
(2/3)n - 5 = 1
½y = -¾y - 40
½x - (5/3) = -½x + (19/4)
¾[(4/5)x - 2] = 11/4
B. Solving Equations with Decimals
  1. Multiply each term on both sides of the equation by 10, 100, 1,000, etc. to get whole numbers. In some situations you may have to simplify the equation before multiplying on both sides.
  2. Every term in the equation must be multiplied by the same number.
  3. Follow the same steps for solving equations as in Sec. 3.3.
  4. If the directions ask you to round the answer but it comes out a fraction, do the division and perform rounding as given in Sec. 1-1.
In the following examples, give your answer to the nearest hundreth.
ExamplesExamples:
4.65x - 4.79 = 13.57 - 6.84x
19.6x - 38.19 = 0.46x + 3.9
–2(4.36 - 6.92x) = 9.27x + 3.87
4.21x + 5.39 = 12.07(2.01 - 4.72x)



G Redden

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