Pharmacy Calculations January 16 2015 Roman Numerals Roman

Pharmacy Calculations January 16, 2015

Roman Numerals

Roman Numerals �I =1 �V = 5 �X = 10 �L = 50 �C = 100 �D = 500 �M = 1000

Roman Numerals �Rule 1 : Roman numerals are never repeated more than three times in a row. �Example: ◦ 5=V

Roman Numerals �Rule 2 : When a Roman numeral is repeated, or when a smaller digit follows a larger number, their values are added together. �Examples: ◦ VII = 5 + 1 = 7 ◦ III = � 1 + 1 = 3 ◦ XXXI = � 10 + 1 = 31

Roman Numerals �Rule 3 : When a smaller numeral comes before a larger numeral, the one of lesser value is subtracted from the larger value. �Example: ◦ IV = (1, 5) = 5 – 1 = 4 ◦ VL = �(5, 50) = 50 – 5 = 45 ◦ XL = �(10, 50) = 50 – 10 = 40

Roman Numerals �Rule 4 : When a numeral of smaller value comes between two numerals of larger value, the subtraction rule is always applied first, and then the addition number. �Examples: ◦ XIV = (10, 1, 5) = 10 + (5 – 1) = 14 ◦ CVL = �(100, 5, 50) = 100 + (50 – 5) = 145

Examples � IX = � IC = ◦ 9 ◦ ◦ Not valid! I can only be subtracted from V and X X can only be subtracted from L and C C can only be subtracted from D and M � DC = ◦ 600 � CCXIX ◦ 219 =

Examples � 7 = ◦ VII � 12 = � 25 = ◦ XII ◦ XXV � 180 = ◦ CLXXX

Examples �XLIX = 49

Ratios/Fractions �Ratios and fractions are two different ways to represent the same relationship �Ratios show the relationship of two numbers separated by a colon. ◦ 5 : 6 (“ 5 to 6”) �Fractions show the relationship of two numbers separated by a line. ◦ 5/6 (“ 5 over 6”) � 5: 6 = 5/6 = “ 5 to 6” = “ 5 over 6”

Ratios/Fractions �Convert ratios: the following from fractions to ◦ 3/4 = 3: 4 �“ 3 over 4 is/equals 3 to 4” ◦ 2/5 = 2: 5 �“ 2 over 5 is/equals 2 to 5” ◦ 4 = 4: 1 �“ 4 is/equals 4 to 1” �How would you read these “sentences” out loud?

Ratios/Fractions �Covert the following from ratios to fractions: ◦ 4: 5 = 4/5 ◦ 6: 8 = � 6/8 ◦ 1: 30 = � 1/30

Proportions �Proportions are two or more equivalent ratios or fractions separated by “: : ” or “=“ that represent the same value

Proportions �Write a proportion equal to the following: ◦ 4: 5 : : � 8: 10 : : 12: 15 ◦ 2/3 : : � 4/6 : : 6/8 ◦ 5: 6 = � 10: 12 = 15: 18

Proportions �Write the simplest proportion (using the smallest numbers) equal to the following: ◦ 5/10 : : 1/2 ◦ 75: 100 = � 3: 4

Proportions �For every 5 songs Taylor Swift writes, 2 of her songs reach number one on the charts. If Taylor writes 20 songs this month, how many would we expect to reach number one? ◦ Hint: set up a proportion � 5: 2 = 20: 8