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Review of Addition and Subtraction of fractions and Introduction to Simplifying Complex Fractions

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Title: 10.5 Addition, Subtraction, and Complex Fractions Last modified by: Allan H. Bredenfoerder Document presentation format: On-screen Show Other titles – PowerPoint PPT presentation

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Title: Review of Addition and Subtraction of fractions and Introduction to Simplifying Complex Fractions


1
Review of Addition and Subtraction of fractions
and Introduction to Simplifying Complex
Fractions
2
Review of Addition, Subtraction of Fractions
  • To add or subtract rational expressions, a common
    denominator is necessary...
  • Example Simplify

Find the LCD 6x
Now, rewrite the expression using the LCD of 6x
Simplify...
Add the fractions...
19 6x
3
Lets try one with polynomials as denominators...
  • Example Simplify

Find the LCD
(x 2)(x 2)
Rewrite the expression by multiplying the top and
bottom of each fraction by whatever is required
to get the LCD of (x 2)(x 2)
Simplify... (watch out for the negative!)
5x 22 (x 2)(x 2)
4
Complex Fraction a fraction with a fraction in
the numerator and/or denominator.
  • Such as
  • How would you simplify this complex fraction?
  • Multiply the top by the reciprocal of the bottom!

5
Method 1For simplifying Complex Fractions
  • Work on the numerator and denominator separately.
  • Find the common denominator of the fractions on
    the top and combine them.
  • Find the common denominator of the fractions on
    the bottom and combine them.
  • Invert the bottom and multiply by the top.
  • Simplify where possible.

6
Example
Invert the bottom and multiply
7
Another Example
8
Yet another example
9
Method 2 For simplifying Complex Fractions
  • To simplify complex fractions, find the LCD of
    all the little fractions
  • Multiply every term by the LCD of all the little
    fractions ...
  • Simplify
  • Divide out where you can ...

10
  • Example Simplify

Using Method 2 To simplify complex fractions,
find the LCD of all of the little fractions
12x
Multiply every term by the LCD...
12x 1
12x 1
Simplify (divide out where you can )...
12x 1
12x 1
12
18
4
9
30 13
11
Here is a complex fraction with polynomials using
method 2 ...
  • Example Simplify

LCD of all of the little fractions
x(x 2)
Multiply every term by the LCD...
x(x 2) 1
Simplify (divide out where you can )...
x(x 2) 1
x(x 2)
x
6x2 12x
4x 8
x 6x2 16x 8
12
The final example explores a problem that has a
fraction as one of its terms in a deep layer.
The method in question solves the equation from
the innermost fractions to the outer layer, by
finding the LCDs of that layer.
13
Example Simplify
Step 1. Group and expand each fractional term.
Step 2. Find the LCD of the innermost fraction.
Step 3. Simplify.
Step 4. Add fractions
Step 5. Invert and multiply.
14
Example (continued)
Step 6. Rewrite with LCD in both terms.
Step 7. Multiply and combine the fractions. At
the end , check to see if there are common
factors in the numerator and denominator that can
be used to reduce.
This is the final solution because there are no
common factors in the problem.
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