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Fractions
4.4.e Writing Equivalent Fractions
equivalent fractions are fractions of equal size with a
new
denominator. Multiply the original fraction by the same factor in
numerator and denominator to produce the new denominator
Write the following fractions as equivalent
fractions of the new denominator.
4.5 Adding and Subtracting Unlike Fractions
4.5.a Adding and Subtracting Unlike Fractions
Find the LCD of all the denominators
Write each original fraction as an equivalent
fraction with a denominator of the LCD
Add or subtract the equivalent fractions
Simplify, if possible
4.5.a examples
4.5.b Write fractions in order
To compare the size of two fractions:
Find the LCD for all fractions
Convert all fractions to the equivalent
fraction using the LCD
Insert the inequality sign between the
original fractions
Examples:
Insert < or > signs between the two fractions to
form a TRUE statement
4.5.c Evaluating Expressions Given Fractional
Replacement Values
Evaluate using the given (x,y) replacement
values of :
4.5.d Solving Problems by Adding or Subtracting
Unlike Fractions
Solve and check the following
4.5.d (Solving Equations Containing Fractions
i.e. Perimeters:)
22. Triangle : with sides of:
23. Rectangle :
4.5.d (Solving Problems by Adding or Subtracting
Unlike Fractions)
1.A sloth travelsmph in
a tree, and 7/10 mph on land .
How many more times faster is it in a tree than on land?
2.The US PO and the Japanese PO handles of the world's mail.
The Japanese PO handles 3/59 of the world's mail.
What fraction is handled by the US PO?
4.6 Complex Fractions and Review of Order of
Operations
4.6.a Simplifying Complex Fractions
Complex Fractions:
Fractions with fractional numerators, fractional
denominators, or both.
Simplify the numerator and denominator
fractions into simple fractions.
Divide the two simple fractions.
4.6.a Examples:
4.6.b Reviewing the Order of Operations to simplify
expressions:
Please, Excuse, My Dear, Aunt Sally
First: Simplify terms Inside Parentheses or other
Grouping Symbols
Then: Exponents and Square Roots
Next: Multiplication, Division, LEFT to RIGHT
Last: Addition, Subtraction, LEFT to RIGHT
4.6.c Evaluating Algebraic Expressions
Evaluate
if
4.7.a Graphing fractions and Mixed
Number s
Remember...
means so
this is graphed to the right of 2 on the number line
means ,
so this is graphed to the left of 3 on the number line
4.7.b Multiplying or Dividing with Mixed
Number s or Whole Number s
4.7.c Adding or Subtracting Mixed Numbers
Find the LCD of the fractional part
Add the whole numbers
Add the fractions
Simplify.
Mixed numbers can be added in horizontal or
vertical format
i.e. Problems of the type:
4.7.d Solving Problems Containing Mixed Number s
12. A sidewalk is made using paver bricks that are
inches wide.
If the installer places 6 bricks side by side, what is
the length of the sidewalk?
13. A bookcase is to be
feet tall and contains 6 equally spaced shelves.
How far apart are the shelves?
14. A small plane used
gallons of fuel in a hour trip.
How many gallons were used per hour?
4.7.e Operating on Negative Mixed Numbers
Rewrite a negative mixed number as a negative
improper fraction:
means which becomes
which can be written as
(4.7.e)Examples:
(i) Write the following as an improper fraction
(ii) Write the following a a mixed number.
(iii) Perform the following operations with mixed
numbers.
4.8 Solving Equations Containing Fractions
4.8.a Solving Equations Containing Fractions
Examples: Solve each of the following for the
unknown
4.8.b Solving Equations by Multiplying by the LCD
Multiply both sides by the LCD to remove
denominators.
Use PEMDAS methods to simplify
Use the addition property to move all terms with
variables to one side of the equation, all terms
with constants to the other
Use the multiplication property to solve for the
variable
4.8.b Examples:
4.8.b Solving Equations containing Fractions:
4.8.c Review of Adding and Subtracting Fractions
Be sure to know the difference between solving an
equation containing fractions and adding or subtracting
two fractions.
Equations contain the '=' sign!
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