Solving Fractional Equations



Name: ____________________________________ Period: _____

Packet 20: Solving Fractional Equations

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Example:

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Step 1: Find the least common denominator

The least common denominator is _______

Step 2: Multiply every term in the equation by the least common denominator

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Step 3: Reduce each term to create a “denominator free” equation

Step 4: Solve for the variable using the steps to solve an equation

Let’s Try It!

Remember to follow the four steps

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Fractional Equations Practice

Follow the four steps to solve the following equations. Show all of your work!

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Fractional Equations Homework

Follow the four steps from class to solve the equations below. Show all of your work and make sure to put a box around your answer.

|1) [pic] |2) [pic] |

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If there is only 1 fraction in the equation:

1st: Multiply EVERY piece of the equation by the denominator of that fraction.

2nd: The fraction will disappear and you can proceed as usual!

|1) [pic] |2) [pic] |3) [pic] |

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If there are 2 or more fractions in the equation:

1st: Find the Least Common Denominator (LCD) of all of the denominators

2nd: Multiply EVERY piece of the equation by the LCD

*Remember to put all (binomials in parentheses) before multiplying!

3rd: Simplify and solve!

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|☼ Make sure you distribute and watch out for the negative! | |

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Fractional Equations Homework

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|3) [pic] LCD: ___ |4) [pic] |

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|5) [pic] |6) [pic] |

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|7) Solve for x: |8) Using order of operations, evaluate: |

|5x – (x + 3) = 7 + 2(x + 2) |3[4 – 8 + 42(2 + 5)] |

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9) Perform the indicated operation and express your answer in scientific notation:

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Match each equation with the property it illustrates.

Properties may be used more than once!

|___10) 6 + (10 + 8) = (6 + 10) + 8 |A) Additive Identity |

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| |B) Additive Inverse |

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| |C) Associative Property |

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| |D) Commutative Property |

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| |E) Distributive Property |

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| |F) Multiplicative Identity |

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| |G) Multiplicative Inverse |

|___11) 6 + 10 = 10 + 6 | |

|___12) –10 + 0 = –10 | |

|___13) [pic] | |

|___14) 7(x – 13) = 7x – 91 | |

|___15) 0 + 16 = 16 | |

|___16) 20 + (–20) = 0 | |

|___17) 3(2) = 2(3) | |

|___18) 5(6 • 3) = (5 • 6)3 | |

|1. − 8x − 2 = − 26 |2. − 1.5 = 0.5x + 7 |

|3. ( 5x + 1 ) – ( 2x – 6 ) = 7 |4. 6x + 1 [pic] 3x − 10 = − 63 |

|5. 3 ( 2x – 1 ) = 7x + 2 |6. 4x − ( 6x – 8 ) = x + 18 |

|7. [pic] + 6 = 8 |8. [pic] − [pic] = 2 |

|9. [pic] − [pic] = − 17 |10. [pic] + [pic] = [pic] |

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We want to “get rid” of the denominators!

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or for the equation

Step 2: Multiply every term in the equation by the least common denominator

Step 3: Reduce each term to create a “denominator free” equation

Step 4: Solve for the variable using the steps to solve an equation

LCD: ___

LCD: ___

LCD: ___

LCD: ___

LCD: ___

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