Fraction Number Concepts – Basic 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.
Addition of Fractions Like Denominators 2/7 + 3/7 = 5/7 2/9 + 5/9 = 7/9 What about different denominators? 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 What about different denominators? 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 Concepts – Basic 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 Add and Subtract 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