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Name: ____________________________________ Period: _____Packet 20: Solving Fractional

Equations

Example:

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

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

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

We want to “get rid” of the denominators!

Step 1: Find the least common denominator 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

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Let’s Try It!Remember to follow the four steps

(1)

(2)

(3)

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Fractional Equations PracticeFollow the four steps to solve the following equations. Show all of your work!

1) 2)

3) 4)

5)

3

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) 2)

3) 4)

5) 6)

4

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) 2) 3)

If there are 2 or more fractions in the equation:1st: Find the Least Common Denominator (LCD) of all of the denominators2nd: Multiply EVERY piece of the equation by the LCD

*Remember to put all (binomials in parentheses) before multiplying!3rd: Simplify and solve!

4) 5) 6)

5)

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

6)

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LCD: ___ LCD: ___ LCD: ___

LCD: ___ LCD: ___

1) 2) 3)

4) 5) 6)

7) 8) 9)

Fractional Equations Homework

1) 2)

6

3) LCD: ___ 4)

5) 6)

7) Solve for x: 5x – (x + 3) = 7 + 2(x + 2)

8) Using order of operations, evaluate:

3[4 – 8 + 42(2 + 5)]

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

B) Additive Inverse

C) Associative Property

D) Commutative Property

E) Distributive Property

F) Multiplicative Identity

G) Multiplicative Inverse

___11) 6 + 10 = 10 + 6

___12) –10 + 0 = –10

___13)

___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

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

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

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

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7. + 6 = 8 8. − = 2

9. − = − 17 10. + =

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