Section 3.5 Solving Equations with Fractions
(If you need to review topics with fractions, please see Appendix A
for help.)
We can use the what was done/undo method with fractions as long as
we know how to work with them.
EXAMPLE:
A method that makes our equations easier to work with is called
"Clearing the Fractions."
1. Find the least common denominator (LCD) of all fractions in the
equation.
2. Multiply both sides of the equation by the LCD. (You can write it as
LCD to keep your fractions lined up correctly.)
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3. Simplify (reduce) each fraction by dividing the denominator into
the LCD and multiply the numerator by what's left.
(fractions should be gone now!)
4. Solve the new equation.
EXAMPLE: Let's redo the problem from before with this method:
Note: Clearing Fractions only works with equations.
It does NOT work with expressions.
Also Note: We are using the LCD to clear the fractions.
We are NOT actually getting a common denominator.
Therefore we multiply by LCD only.
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(see page 267 warning)
EXAMPLES: Clear the fractions and solve each equation. Check the answers by substituting.
a)
b)
c)
Clearing Fractions and Combining Like Terms:
EXAMPLES: Clear the fractions and solve each equation. Check the
answers by substituting. (Let's use the calculator to check this time!)
Writing and Solving Equations with Fractions:
EXAMPLE: For the following situation,
• Choose a letter to represent the variable quantity
• Translate the problem into an equation
• Solve the equation by clearing the fractions
• Check the solution in two ways
Two-thirds of the students in a MTH 60 class took their module test on
Monday and another one-fourth of the students took the test on
Tuesday. If 33 students have tested so far, how many students are
enrolled in the MTH 60 class?