Ratios, Percents, Simple Equations, & Ratio-Proportion Chapter 2 MAT 119

Objectives Interpret values expressed in ratios Convert among fractions, decimals, ratios and percents Compare the size of fractions, decimals, ratios, and percents Determine the value of X in simple equations Set up proportions for solving problems Cross-multiply to find the value of X in a proportion Calculate the percentage of a quantity

Introduction Health care professionals need to understand ratios and percents to be able to interpret, prepare, and administer accurately a variety of medications and treatments.

Ratios Like a fraction, a ratio is used to indicate the relationship of one part of a quantity to the whole. Ratios can be written as a fraction or separated by a colon. Example: On an evening shift, if there were 5 nurses and 35 patients, what is the ratio of nurses to patients? 5 nurses to 35 patients – 5 nurses per 35 patients 5 = 1 which is the same as 5:35 or 1:7 35 7

Ratio Math Tip In a ratio, the numerator is always to the left of the colon, and the denominator is always to the right. Example: Adrenalin 1:1000 for injection means there is one part Adrenalin per 1000 total parts of solution. This is also called the concentration of a drug.

Convert Ratio to Fraction The colon in a ratio is equivalent to the division sign in a fraction

Convert Ratio to Decimal To change a ratio to a decimal Convert ratio to a fraction Divide numerator by denominator

Percents Percent is a type of ratio. The word comes from a Latin phrase per centum, meaning per hundred. This means per hundred parts or hundredth part The % symbol means ___/100 Example: 3% = 3/100 = 0.03

Percents To remember the value of a given percent Example: Replace % symbol with “/” for per and “100” for cent Example: “20% said ‘yes’ in the survey,” that means 20 per 100 said “yes” 20% may be written as 20/100 (reduced to 1/5)

Converting among Ratios, Percents, Fractions, and Decimals The relationship is important to understand to easily convert from one to another See Rules on p. 65 Percent to a fraction Percent to a ratio Percent to a decimal Decimal to a percent Ratio to a percent

Convert Percent to Fraction To change a percent to a fraction Drop % sign Place remaining number as the numerator over denominator 100 Reduce to lowest terms

Convert Percent to Fraction, Contd’ Reduce fraction to lowest terms Think: per (/) cent (100)

Convert Percent to Ratio To change a percent to a ratio Convert percent to a fraction in lowest terms Place numerator to left of colon and denominator to right of colon

Convert Percent to Decimal To change a percent to a decimal Drop % sign Divide by 100 4% = 4 ÷ 100 = 0.04

Convert Decimal to Percent To change a decimal to percent Multiply by 100 Add % sign 0.5 x 100 = 50%

How to Remember These? Think PDL (Percent to Decimal, Left) DPR (Decimal to Percent, Right)

Convert Ratio to Percent To change a ratio to a percent First convert ratio to a fraction Convert resulting fraction to a decimal and then to a percent

Convert Ratio to Percent (Continued)

Proportion Two ratios that are equal or an equation between equal ratios Math Tip A proportion is written as two ratios separated by an equal sign or a double colon

Ratio-Proportion 5 : 10 :: 10 : 20 The above reads 5 is to 10 as 10 is to 20

Proportion Can be written 2 ways Extremes and Means a : b :: c : d The "means" are the inside terms, b and c, and the "extremes" are the outside terms, a and d Or written: a/b = c/d a = c b d

Proportion Cross-Products If two fractions are equivalent, or equal, then cross-products are also equal

Solving for X in a Proportion 1 = x So, 1 x 8 ÷4=2 𝑋=2! 4 8

Comparing Percents and Ratios Solutions that are administered use concentrations as a percent or ratio IV (intravenous) solutions: 0.9% versus 5% Which is larger? 0.9% = 0.9 parts of the solid per 100 total parts 5% = 5 parts of the solid per 100 total parts 5% is larger that 0.9%

Ratio Word Problems Adam and Kimberly shared a cash prize in the ratio 5:3 Adam received $150 How much money did Kimberly receive? 5:3 means parts to parts (each part of equal value) X = 90

Solving…. Adam to Kimberly 5:3; How much money did Kimberly receive? Adam: 5 parts Kimberly: 3 parts $30 $30 $30 $30 $30 = $150 $30 $30 $30 = $90

Ratio Word Problems The ratio of boys to girls in the computer club is 4:5 Altogether are 36 students in the club How many girls are there? X = 20

Solving…. 36 students boys to girls 4:5- how many are girls? Boys: 4 parts Girls: 5 parts 20 Girls! 9 parts = 36 4 4 4 4 1 part = 4 4 4 4 4 4

Ratio Word Problems If the ratio of saturated to unsaturated fatty acids in a cell membrane is 9 to 1, and there are a total of 69 billion fatty acid molecules, how many of them are saturated?

Solving… saturated to unsaturated 9:1; total 69 billion; how many are saturated? Saturated – 9 parts Unsaturated – 1 part 62.1 billion saturated fatty acids in a cell membrane 10 parts = 69 billion 1 part = 6.9 billion 9 x 6.9 = 62.1 billion

The Percentage of a Quantity Percentage (Part) = Percent x Whole Quantity Example: What is 12% of 48? (of means multiply)

Percentage of a Quantity (Continued) What is 8% of 200? 0.08 × 200 = 16 How much is 4% of 30? 0.04 × 30 = 1.2

Finding Percent using Ratio/Proportion Percentage (part) = Percent Whole Quantity 100 What percent of 420 is 105? 105 = 420 X% 100% (p)X = 25%

Problems 2.1% of what number is 525? 25,000 7% of 2100 is what number? 147 What % of 9 is 7.2? 80%

Percentage Word Problems In one week 96 patients seen at a local medical group were sick with the flu. If this were 64% of the total number of patients seen, how many patients were there altogether? 150

More Word Problems According to 2002 data gathered by the Delaware Division of Public Health, 23% of people in Kent County smoke daily. In a group of 400 people from Kent County, how many people would it be likely to find that smoke daily? of = multiply

More Word Problems An 80 gram tube of ointment contains 1.6 grams of a certain medication. What percent of the total weight of the ointment is the drug?

More Word Problems In order to take most of the clinical nursing classes, students at Terry Campus, Delaware Tech, must pass a “pre-clinical math test” administered at the beginning of the class in order to continue with the clinical nursing class they are enrolled in. Each student must obtain a score of 85% on the “pre-clinical math test”.

Continued If Julie took the quiz which had a maximum of 20 points and earned 15 points, did Julie earn the minimum requirement of an 85%? What percent did she score? NO! She must take a 2nd test & MUST pass 15 points = 75% (Each point is worth 5%) How many points can she MISS and still pass?? 3 points = 15% = 85% PASSED

More Word Problems A patient was to be administered 20 mL of a particular medication at 8:00 A.M and receive 40% more than that amount at 10:00 A.M. How much should the patient be administered at 10:00 A.M.? 40% x 20 mL = 8 mL 20 mL + 8 mL = 28 mL to be given @ 10:00 A.M.

More Word Problems A patient has been recommended by his doctor to lose some weight to lower his risk for heart disease. So far, the patient has lost 30% of the amount of weight that he has set as a goal for him to lose. If the patient has lost 12 kg (kilograms), how much weight did he set as a goal to lose?

Solving…

More Word Problems The cost of an experimental drug this year was $2.40 per mL. If the cost is expected to decrease by 35% next year, how much will the drug cost next year? 35% x $2.40 = $0.84 (amount of decrease) $2.40 - $0.84 = $1.56/mL

More Word Problems Because he has Blue Cross / Blue Shield as his primary insurance, Les receives a 12% discount on prescription drugs from his local pharmacy. If the amount of the discount Les received the last time he got prescription drugs was $4.20, what was the cost of his prescription?

Solving…

More Word Problems The flow rate of an IV drip containing saline is set at 70 mL/hr at 2:00 P.M. Each 10 minutes thereafter the rate is to be increased by 10% of the previous rate. What will the flow rate be at 2:30 P.M.? (Round final answer to whole number.)

Solving… 2:00 pm – IV rate is 70 mL/h 2:10 pm – 70 x 10% = 7 Final answer rounded to whole number = 93 mL/h (IV pumps speak in whole numbers…more on this later)

Practice! Change 2 2/3% to a fraction and reduce to lowest terms 1/5 X 10 = ? 2/3 2 1/2 X 3/5 = ? 2% 1/4 28% X 1 1/5 = ?