1. 3.1 Ratios Ratio – quotient of two quantities with the same units or can be converted to the same units Examples: a to b, a:b, or Note: percents are ratios where the second number is always 100:

2. 3.1 Ratios Simplifying a ratio: –Convert both quantities to the same units if necessary –Convert from decimals to whole numbers if necessary –Reduce to lowest terms

3. 3.1 Rates Rate - like a ratio except the units are different (example: 50 miles per hour) To simplify a rate: –Reduce as is and leave the unit names –Rates can be expressed as a decimal or fraction

4. 3.2 Proportions two rates or ratios are equal where a,d are the extremes and b,c are the means For a proportion to be true: product of the means = product of the extremes

5. 3.2 Proportions To solve a a proportion, use cross- multiplication Proportion: Cross multiplication: solve

6. 3.2 Proportions Solve for x: Cross multiplication: so x = 63

7. 3.3 Converting Ratio Strength and Percent Strength Ratio Strength: fraction comparing the amount of medication by weight in a solution to the total amount of solution Percent Strength: amount of grams of medication in 100ml of solution

8. 3.3 Converting Ratio Strength and Percent Strength To convert ratio strength to percent strength: –Ratio strength (in g/ml) is one side of proportion –Put on the other side of the proportion –Solve the proportion –Place a percent sign after the solution

9. 3.3 Converting Ratio Strength and Percent Strength Example: 24 ml of solution contains 6 grams of medication. What is the percent strength?

10. 3.3 Converting Ratio Strength and Percent Strength Converting percent strength to ratio strength: –Place the percent strength without the percent sign over 100 –Convert if necessary to a ratio of 2 whole numbers –Reduce the fraction to lowest terms

11. 3.3 Converting Ratio Strength and Percent Strength Example: Convert percent strength of 25% to a ratio.

12. 4.1 Apothecaries’ System Apothecaries’ measures came into use by the apothecary, one who prepared and sold compounds for medicinal purposes. Some institutions and physicians still use apothecaries’ measures. The Pharmaceutical Association “went metric” in 1959 – so this system is for the most part obsolete.

13. 4.1 Apothecaries’ System Apothecaries’ measures: weights – 1 grain = weight of a drop of water

14. 4.1 Apothecaries’ System Apothecaries’ measures: volume – 1 minim = volume of a drop of water; the abbreviation for drop is gtt.

15. 4.2 Household System Household measures: volume – liquid medications (again a drop is abbreviated gtt.)

16. 4.3 Abbreviations and Symbols UnitAbbreviationSymbol gallongal.C. quartqt. pintpt.O. ounceoz.See book dramdr.See book graingr. minimmin.See book

17. 4.3 Abbreviations and Symbols UnitAbbreviationSymbol dropsgtts. poundlb.# teaspoontsp.t tablespoonTbl. or Tbs. or Tbsp.T cupc.c

18. 4.3 Abbreviations and Symbols – Roman Numerals

19. 4.4 Charted Dosages Charting in Apothecaries’ System Main rule: symbol or abbreviation – then amount in Roman numerals Exceptions: Fractions – fraction in Arabic (not Roman) Amount > 40 – amount in Arabic & reverse order Household – amount in Arabic & reverse order using abbr.

20. 4.4 Charted Dosages Example: what is the meaning of the charted dosages: dr. v t.i.d. – 5 drams 3 times a day oz. iii q. 4h. – 3 ounces every 4 hours min. viss b.i.d. - minims 2 times a day

21. 4.5 Converting Units within Apothecaries’ System Using Factor-label Method to convert. Example: express 3 yards in feet

22. 4.5 Converting Units within Apothecaries’ System To convert from one unit to another 1.Write down amount from which you are converting 2.Put an “X” and draw a fraction bar 3.Put “old units” on bottom and “new units” on top 4.Find the conversion from the table 5.Solve:

23. 4.5 Converting Units within Apothecaries’ System Example: Convert 5 gallons to pints Notice how the units “cancel”

24. Supplement 2.1 Using Formulas A = lw I = prt A = ½bh d = rt Area of rectangle Interest Area of triangle Distance formula C-F Temperature Conversion F-C Temperature Conversion

25. Supplement 2.1 Using Formulas Example: d = rt; (d = 252, r = 45) then 252 = 45t divide both sides by 45:

26. Supplement 2.2 Solving a Formula for a Specified Variable Example: Solve the formula for B multiply both sides by 2: divide both sides by h: subtract b from both sides: