**Definitions**

Fraction: a part of a whole.

Numerator: number of parts being considered.

Denominator: number of equal parts of the whole.

Example: |
numerator |

denomin ator |

The graph of 3/4 on a number line :

__Types of Fractions__

Proper fraction: the numerator is less than the

denominator.

Example:3/4

Improper fraction: the numerator is greater than or

equal to the denominator.

Examples:6/6 and 9/5

Mixed Number: a whole number and a proper fraction.

Example: means

** Division by 0 and 1**

Zero divided by any number is 0. Division by 0 is

undefined.

Examples:0/9 = 0 and 7/0 =undefind

Any number divided by itself is 1:

Example:6/6 = 1 and x/x = 1

**Writing Fractions and Mixed Numbers**

The number 1 can be written as any fraction:

Example:

To write a whole number as a fraction, write the

whole number over 1:

Example:4 = 4/1

To write a mixed number as an improper fraction,

multiply the whole number by the denominator, add

the numerator, and keep the denominator:

Example:

To write an improper fraction as a mixed number,

divide the numerator by the denominator. Use the

quotient to write the whole number. Place the

remainder in the numerator of the fraction, and keep

the denominator.

Example:

**Divisibility Rules**

Rule for 2: If a number ends in 0, 2, 4, 6, or 8 (even

number), divide by 2.

Rule for 3: If the sum of a number ‘s digits is a multiple

of 3, divide by 3.

Rule for 5: If a number ends in 0 or 5, divide by 5.

Rule for 10: If a number ends in 0, divide by 10.

**Prime Factorization**

A prime number can only be divided by itself and 1.

Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ...

To prime factor a number , divide the number by 2, 3,

5, 7 ... Then write the number as a product of its

prime factors.

Example:

60 = 2• 30

= 2• 2• 15

= 2• 2• 3• 5

= 2^{2}• 3• 5

** Simplifying Fractions **

A fraction is simplified when the numerator and

denominator have no common factors other than 1.

To simplify a fraction, factor the numerator and the

denominator. Cancel common factors and write a 1

in the numerator where necessary.

Example:

Example:

**MULTIPLYING & DIVIDING FRACTIONS**

**Multiplying Fractions**

1) Change mixed numbers to improper

fractions.

2) Multiply the numerators; multiply the

denominators.

3) Cancel common factors.

Examples:

**Dividing Fractions**

1) Change mixed numbers to improper

fractions.

2) Think KFC:

Keep the __first.__

Flip the __second.__

Change the ope ration to multiplication .

3) Fol low the rules for multiplying.

Examples:

**ADDING & SUBTRACTING LIKE**

FRACTIONS

1) Add or subtract the numerators.

2) __Keep__ the denominator.

3) __Simplify__ the answer if necessary.

__Examples:__

**Adding & Subtracting Mixed Numbers**

Like Denominators

1) Change mixed numbers to improper

fractions.

2) Add or subtract the numerators.

3) Simplify the answer.

Examples:

** Finding the Least **

Common Denominator (LCD)

List the multiples of the larger

denominator to find the LCD.

Example: Find the LCD of 5/6 and 3/8.

The LCD is 24 because 24 is the

smallest common multiple of 6 and 8.

Multiples of 8: 16, 24

Multiples of 6: 12, 18, 24

**Writing Equivalent Fractions with**

the LCD

To write an equivalent fraction with the

LCD, multiply the fraction by a form

of 1:

__Example:__ Write each fraction with a

with a denominator of 24:

5/6 and 3/8

Multipl 5/6 by 4/4 because 6(4) = 24:

Multiply 3/8 by 3/3 because 8(3) = 24:

**ADDING & SUBTRACTING UNLIKE**

FRACTIONS

1) Find the LCD

2) Rewrite the fractions.

3) Add or subtract the numerators.

4) __Simplify__ the answer.

Examples:

**Adding & Subtracting Mixed Numbers**

Unlike Denominators

1) Find the LCD and rewrite the

fraction parts.

2) Change mixed numbers to improper

fractions.

3) Add or subtract the numerators.

4) __Simplify__ the answer.

Examples: