# FRACTION STUDY GUIDE

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
= 22• 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:

FRACTIONS

1) Add or subtract the numerators.
2) Keep the denominator.
3) Simplify the answer if necessary.

Examples:

Like Denominators
1) Change mixed numbers to improper
fractions.
2) Add or subtract the numerators.

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:

FRACTIONS

1) Find the LCD
2) Rewrite the fractions.
3) Add or subtract the numerators.

Examples:

Unlike Denominators

1) Find the LCD and rewrite the
fraction parts.
2) Change mixed numbers to improper
fractions.
3) Add or subtract the numerators.

Examples:

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