# 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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