4.1.a Identifying Numerators and Denominators

Numerator / Denominator

Numerator รท Denominator

4.1.b Writing Fractions to Represent Shaded Areas of

Figures

4.1.c Graphing Fractions on a Number Line

4.1.c Examples: Graph the following fractions on

a number line:

4.1.d Simplifying fractions of the form:

4.1.e Illustrating Mixed Numbers

**Mixed Numbers:**

A number containing a whole number and

a proper fraction.

4.1.e Writing Mixed Number s as Improper

Fractions

4.1.f Wr iting Improper Fractions as Mixed Number s

or Whole Number s

Divide the denominator into the numerator to produce

a mixed number.

The Whole Number part of the mixed number is the

quotient, the fraction part of the mixed number is the

remainder over the original denominator.

4.2.a Writing a Number as a Product of Prime

Numbers

Finding the Prime Factors using

(a) 'factor tree' or \

(b)successive division by increasing larger

prime numbers

Write the prime factorization of each of the following

numbers

1. 12 2. 48 3. 56 4. 45 5. 240

Determining if a number is divisible by 2, 3, or 5

4.2.b Writing a Fraction in Simplest Form

Write the numerator and denominator in prime

factorization form.

Divide common factors in the numerator and

denominator.

Examples:

4.2.c Determining Whether Two Fractions are

Equivalent

Determine if they are equivalent by Simplifying numerator

and denominator into common factors

Determine if 7/9is equivalent to 21/27

Using Prime Factorization of numerator and denominators of both fractions:

4.2.c (determination of equivalent fractions)

Determine if they are equivalent by Cross Multiplication

If ....

then ....

a*T = b*R

4.2.c Examples: Determine if the following fractions

are equivalent.

4.2.d Solving Problems by Writing Fractions in

Simplest Form

**Examples:**

14. There are 58 national parks in the United States. Six

of these are in Washington state and 2 are in Wyoming.

Determine, in simplest form, the fraction of the parks

located in each state?

15. The outer wall of the Pentagon is composed of 10

inches of concrete, 8 inches of brick, and 6 inches of

limestone. What is the fractional width of (i) the

concrete (ii) the limestone?

4.3.a Multiplying Fractions

Multiply the numerators

Multiply the denominators

Simplify if possible.

**Examples:**

4.3.b Evaluating Expressions with Fractional

Bases

Examples:

4.3. c Dividing Fractions

Invert the fraction in the denominator

Multiply the numerator and inverted

denominator fractions

**Examples:**

4.3.d Multiplying and Dividing with Fractional

Replacement Values

Evaluate

(i) x *y and

(ii) x / y

given the following replacement values for x and y

in (x,y) format.

4.3.e Solving Applications by Multiplying and

Dividing Fractions

**Examples:**

21. How much money is alloted to rent, if 2/3 of the

$450 weekly income is to be used.

22. If soup weighs 5/4 pound per can and a case

contains 24 cans, what is the weight of the

case?

23. How many gallons of liquid are in a 48 gallon vat

if it is filled 7/8 to the top?

4. 4 Adding and Subtracting Like Fractions and

Least Common Denominator

4.4.a Adding or Subtracting Like Fractions

Note:

4.4.a Examples:

4.4.b. Adding and Subtracting Given Fractional

Replacement Values

Examples:

Evaluate each expression for the given replacement

values (x,y,z)

4.4 c Solving Problems by Adding and Subtracting

Like Fractions

Examples:

Find the perimeter.

16. A rectangle with dimensions :

17. A triangle with sides of length:

18. A square with a side length of

(4.4 c) Using the following table:

What fraction of employees are:

19. Not covered by HMO?

20. Use P-o-S or Traditional Fee?

Type of Health Plan | Fraction of Employees Using This Pla n |

HMO | 6/20 |

Point-of-Service | 4/20 |

Prefer red Provided | 7/20 |

Traditional fee-for -service | 3/20 |

4.4.d Finding the Least Common Denominator (LCD)

or Least Common Multiple(LCM)

The LCD is the smallest denominator that is evenly

divisible by ALL denominators in a list of fractions.

: The LCD is '12'

When adding or subtracting unlike fractions, all

must be converted to equivalent fractions of the

same denominator.

( 4.4.d )Finding the LCD for a set of fractions.

Method 1:

Determine if the Largest original denominator is

evenly divisible by ALL denominators in the set of

fractions.

( 4.4.d )Method 2:

Use prime factorization of all denominators. Works

for a list of 3 or more fractions.

For example:

Expressing 1/6 as a fraction with a denominator

consisting of a product of only prime numbers is as

follows.

Note that the new denominator is a product of only

prime numbers.

( 4.4.d )The LCD is a number composed of

ALL unique prime factors appearing in ALL

prime factorization of the denominators

Each prime number factor will appear the

same number of times as the maximum

number found in ANY ONE of the prime

factorizations.

( 4.4.d )Example:

Find the 'prime factorization of ALL denominators of

the following fractions:

Prime Factorization of the denominators:

( 4.4.d )Note:

The LCD is the product of Every Different Prime

Number appearing in the prime factor ization of the

denominator s. (2*3*5)

Each of these unique prime number factor s is raised to

a power equal to the Maximum Number of Occurrences

of that prime number in any one of the factorizations.

This is demonstrated by the exponents of all unique

prime number factor s denoting the maximum number

of coinsurances of each.

4.4.d Examples: Find the LCD of the following sets

of fractions: