Definitions - A fraction means to divide. 1/4 means 1 divided by 4. 1 numerator - 4 denominator :RA 3/4 is a proper fraction, read: "three fourths". Note: the whole has been divided into 4 equal parts and 3 parts are being taken. .75 is a decimal fraction. Note: the whole has been divided into 100 equal parts and 75 parts are being taken. It is read: "seventy five hundredths". 3 75 - = --- = .75 4 100 :RA To convert 3/4 to 75/100, you raise 3/4 to higher terms by multiplying both numerator and denominator by the same number 25. 3 25 75 - x -- = --- 4 25 100 This is called an equivalent fraction. You can multiply the numerator and denominator of a fraction by the same number (except 0) without changing the value of the fraction. :RA To convert 75/100 to 3/4, you reduce 75/100 to lower terms by dividing both numerator and denominator by the same number 25. 75 25 3 --- / -- = - 100 25 4 Shortcut: cancellation of common factors. The fraction 3/4 can also be considered: a. As the division of 3 by 4; or b. As the multiplication of 3 by 1/4. :RA An Improper Fraction such as 5/4, is greater than 1. This is so because the numerator is greater than the denominator. The value of 5/4 is the same as that of the mixed number 1 1/4. 5/4 = 1 1/4 Note: Answers to all Fraction Problems must be reduced to lowest terms. :RA Addition And Subtraction of Fractions: The sum of 2 fractions which have the same denominator is a fraction with the same denominator and with a numerator which is the sum of the original numerators. :RA If the fractions to be combined have different denominators change the original fractions into equivalent fractions with a LCD as the new Denominator. The Numerator and Denominator are multiplied by the same number to change each fraction to higher terms. 3 1 3 - 1 2 1 - - - = ----- = - = - Ans. 8 8 8 8 4 3 1 11 - - - = -- Ans. 4 5 20 Note: Here you are required to use LCD 20. :RA Multiplication And Division of Fractions Multiply numerators to obtain the new numerator, and multiply denominators to obtain the new denominator; 5 4 20 1 - x -- = --- = - 8 15 120 6 :RA Note: Cancellation simplifies your work. You may divide any numerator and any denominator by their common factors. 5 4 - x -- 8 15 Then proceed as above: 1 1 1 - x - = - Ans. 2 3 6 :RA To multiply mixed numerals - first convert them to improper fractions. To divide a fraction by a fraction, invert the divisor and then multiply. 1/2 1/2 3 --- = --- = - 1/3 3/1 2 To divide mixed numerals, convert to improper fractions first. :RA Complex Fractions A complex fraction has one or more fractions in its numerator or denominator. To simplify, find the LCD of all fractions in numerator and denominator Then multiply the numerator and denominator of the complex fraction by the LCD. 2 5 - + - 3 6 ------ 3 - 8 :RA Order of Operations First perform multiplication and division from left to right, and then perform addition and subtraction from left to right. 100/10 - 8 x 1/2 = 10 - 4 = 6 :RA Decimals A decimal is a fraction whose denominator is a power of 10 (10, 100, 1000, 10,000 etc.) Note: Decimal Form Fraction Form .6 = 6 tenths = 6/10 .05 = 5 hundredths = 5/100 .32 = 32 hundredths = 32/100 .007 = 7 thousandths = 7/1000 :RA Note: 7 3.7 = 3-- 10 2 39-- = 39.2 10 :RA Shortcut: Decimal Numbers: millions hundred thousands ten thousands thousands hundreds tens ones . tenths hundredths thousandths ten thousandths :RA Fraction-Decimal Equivalents (Values are rounded in some cases) 1/2 = 0.50 1/3 = 0.33 1/4 = 0.25 1/5 = 0.20 1/6 = 0.17 2/3 = 0.67 3/4 = 0.75 2/5 = 0.40 5/6 = 0.83 1/8 = 0.125 3/8 = 0.375 5/8 = 0.625 7/8 = 0.875 1/12 = 0.83 5/12 = 0.416 7/12 = 0.583 11/12 = 0.916 :RA 1/16 = 0.0625 3/16 = 0.1875 5/16 = 0.3121 7/16 = 0.4375 9/16 = 0.5625 11/16 = 0.6875 13/16 = 0.8125 1/20 = 0.05 1/25 = 0.04 1/50 = 0.02 :ET :ET
