Fraction Number ConceptsBasic College Mathematics for Teachers

Reference:  K. Elayn Martin-Gay – Page 1        Definition:  Fraction

Fraction as Components

Definition: Part of a Whole

Numerator is Top

Denominator is Bottom

4/5           2/3          5/7

# Fraction as Images

If   # # # # # = 1

Then   # # # = 3/5

If   @ @ @ @ @ @ @  = 1

Then    @ @ @ @  = 4/7

# Proper Fraction

Numerator is smaller than Denominator

Value is less than  1

3/5               5/7              8/9

Proper Fractions are OK

when they are in lowest terms!

# Improper Fraction

Numerator is larger than Denominator

Value is greater than  1

5/3               7/4            9/5

Improper Fractions must be changed

to Mixed Numbers.

## Like Denominators

2/7  +  3/7  =  5/7

2/9  +  5/9  = 7/9

2/3 + 5/6 = ?         2/3 + 4/5 = ?

# Subtraction of Fractions

## Like Denominators

5/7  -  1/7  =  4/7

7/9  -  4/9  =  5/9

5/6 - 2/3 = ?         4/5 - 2/3 = ?

# Multiplication of Fractions

Multiply Tops to get Answer Top!

Multiply Bottoms to get Answer Bottom!

2/3   x   4/5   =   8/15

5/7  x  7/9  =  35/63

Multiply means  of  thus 2/3  of  4/5  = ?

# Division of Fractions

Multiply by the Inverse!

Inverse equals  flip of a fraction!

3/7  /  2/3  =  x / x

3/7  x  3/2  =  9/14

Inverse or Reciprocal  of   3/5   is   5/3

Thomas Love              Malone College              2006/2008

Fraction Number ConceptsBasic College Mathematics for Teachers

Reference:  K. Elayn Martin-Gay – Page 2        Definition:  Fraction

Prime Numbers

Numbers divisible only by

one (1) and self!

Examples for Prime Numbers!

1, 3, 5, 7, 11, 13, etc….

What are some more?

What about Odd and Even Numbers?

# Composite Numbers

Numbers divisible by more than

one (1) and self!

Examples of Composite Numbers!

2,4,6,8,10,12,14,15,16, etc….

Wow!  Really a lot of numbers!

What about Odd and Even Numbers?

Equivalent or Equal Fractions

Compare:  <  =  >

(8)       2/3 < 3/4       (9)

(12)     2/3  =  4/6     (12)

(45)      5/7  >  6/9      (42)

Cross Multiply upwards to Check!

Simplest or LowestTerms

Reduce or Raise (Change)

Change  2/3  to 12ths!

2/3 = 8/12

Multiply  2 & 3  by  4!

Reduce 9/15  to Lowest Terms!

9/15 = 3/5

Divide  9 & 12  by  3!

# Common Multiple

Have you ever played Hide & Seek?

5, 10, 15, 20, 25, etc….

2,4,6,8,10,12, etc….

7, 14, 21, 28, 35, etc….

Think of  Times Table……

# Common Denominator

This concept is critical to

Fractions with  Unlike  Denominators!

2/3 + 5/6    =  4/6  +  5/6

2/3 + 4/5   =   10/15 + 12/15

A lot of Multiplying with this concept!

Least Common Multiple (LCM)

Given two numbers determine

the Least Common Multiple!

Find LCM for 3 & 12

What number does 3 & 12

both go into without a remainder?

36

Least Common Denominator (LCD)

Given two denominators determine

the Least Common Denominator!

Find LCD for 5 & 7

What is the smallest number

3 & 5 both go into without a remainder?

35

Thomas Love              Malone College              2006/2008