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3.1 Ratios

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:. 3.1 Ratios. Simplifying a ratio: Convert both quantities to the same units if necessary

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3.1 Ratios

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  1. 3.1 Ratios • Ratio – quotient of two quantities with the same units or can be converted to the same unitsExamples: 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-multiplicationProportion: 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

  17. 4.3 Abbreviations and Symbols

  18. 4.3 Abbreviations and Symbols – Roman Numerals

  19. 4.4 Charted Dosages • Charting in Apothecaries’ SystemMain rule: symbol or abbreviation – then amount in Roman numeralsExceptions:Fractions – fraction in Arabic (not Roman)Amount > 40 – amount in Arabic & reverse orderHousehold – 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 dayoz. iii q. 4h. – 3 ounces every 4 hoursmin. 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 • Write down amount from which you are converting • Put an “X” and draw a fraction bar • Put “old units” on bottom and “new units” on top • Find the conversion from the table • Solve:

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

  24. 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 Supplement 2.1 Using Formulas

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

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

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