Simplifying Fractions, Ratios, and Percentages: A Math Guide

Mathematical Review - Chapter 10 Amy G Martinez PLEASE SHOW YOUR WORK FOR FULL CREDIT. Each correct answer is worth .5 point. (Total 35 points) Find the simplest form of each of the following fractions: 1. 20/40 = 2/4=1/2 2. 4/6 = 2/3 3. 12/54 =6/27=2/9 4. 8/12= 2/3 5. 16/28 = 4/7 Find the quotient in the following fractions. Round to two decimal places. 1. 2/5 = .40 2. ¾ =.75 3. 7/8 = .88 4. 107/98 = 1.09 5. 54/65 =.83 Round to one decimal place or nearest tenth. 1. 19.76 =19.8 2. 34.623=34.6 3. 172.87= 172.9

4. 99.98 = 100.0 5. 125.969 = 126.0 Round to two decimal places. 1. 8.36801 = 8.37 2. 14.5264 = 14.53 3. 0.87642 = 0.88 4. 27.99999 = 28.0 5. 15.90176= 15.90 Complete the following conversions. Fractions to percentages (round to one decimal place): 1. 5/8 = 0.625 x 100= 62.5% 2. 3/5 = 0.6 x100= 60 % 3. 2/4 = 1/2 = 0.5 x 100= 50% 4. 7/12 = 0.58333 x100= 58.3% 5. 3/15 = 1/5 = 0.2 x100=20 % Decimals to percentages (round to one decimal place): 1. 0.28 = 0.28/1 x 100/100= 28/100= 0.28 = 28%

2.0.07 =0.07/1 x 100/100= 7/100= 0.07= 7% 3. 0.1254= 0.1254/1 x 100/100 = 12.54/100= 0.1257 =12.54% 4. 0.4299 = 0.4299/1 x 100/100 =42.99/1000=4299= 42.99%= 43% 5. 0.9981= 0.9981/1 x 100/100= 99.81/100= 0.9981 = 99.81% Percentages to decimals: 1. 12% = 12/100=0.12 2. 27% = 27/100= 0.27 3. 0.5% = 0.5/100= 0.005 4. 7.5% = 7.5/100= 0.075 5. 3.4% = 3.4/100= 0.034 6. A family practitioner in your local physician’s clinic saw 150 adults in one week for their annual physical examinations. Sixty-seven received the flu vaccine. Express the rate of the flu vaccine administration in percent. Round to one decimal place. 67/150 x 100 = 44.67%= 44.7% Express the following ratios in their simplest form. 1. A group of 15 men and 20 women have diabetes. Express the ratio of men with diabetes to women with diabetes. Calculate it to its simplest form. 15:20 divide both numbers by common factor 5 = 3:4

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2. Your college bookstore reported that of the 1,000 books sold during enrollment, 320 were health information management (HIM) books. Express the ratio of HIM books to the total number of books sold. Calculate to its simplest form. Total # of books sold = 1000 HIM books=320 = 320/1000=32/100= 8/25 3. There are 12 instructors in your HIM program. Five of these are male instructors, the rest are female. Express the ratio of male instructors to women instructors. Calculate it to its simplest form. There is no common factor so ratio is in simplest form 5:7 4. Of the 12 instructors in the previous example, three have a Master’s degree and the rest have a Bachelor’s degree. Express the ratio of Bachelor’s degree prepared instructors to Master’s degree prepared instructors. Calculate to its simplest form. 9:3 divide both # by common factor 3 = 3:1 5. Community Hospital reported sixteen births this past month. Four were male. What is the ratio of male births to female births? Calculate to its simplest form. Divide both # by common factor 4 = 4:12 = 1:3 1. A school district wants to know the proportion of students who have deferrals for mandated vaccines. District School #1 has 237 students. Of the 237 students, 225 students are up to date on their vaccines. There are 12 students with deferrals. What is the proportion of students with deferrals who have not been vaccinated? Round to two decimal places.

12/ (12+225)= 0.05 2. At Community Clinic, 50 patients were seen in one day. Of those, 6 have Type II diabetes mellitus. What is the proportion of people in the group that have Type II diabetes? Express as a decimal and round to two decimal places. 6/(6+44)= 0.12 3. At Community Clinic, Dr. Clark treats only diabetic patients. He has 650 active patients. Of those, 458 have attended his specialized training session for newly diagnosed diabetes. What proportion of Dr. Clark’s patients have undergone his training? Express as a decimal and round to two decimal places. 458/ (458+192) = 0.70 4. At Community Clinic, Dr. Simpson, an interventional cardiologist, saw 270 patients last quarter. Of those, he performed stent procedures on 182 patients. What is the proportion of Dr. Simpson’s patients who have had stent procedures? Express as a decimal and round to two decimal places. 182/ (182 +88)= 0.67 5. Dr. Rutan, an internist in the community clinic above, asked that 14 of the 35 patients he saw last week get their x-rays and lab work completed the day before their appointments. What is the proportion of Dr. Rutan’s patients who had preliminary work completed prior to their appointments? Express as a decimal and round to two decimal places. 14/ (14 +21) = 0.40

1. Community Hospital reported the following birth weights for babies born January 30, 2021: 6.9 lbs, 3.7 lbs, 7.7 lbs, 6.6 lbs, 7.3 lbs, 5.5 lbs, 9.9 lbs, 7.0 lbs, 5.5 lbs, and 7.7 lbs. What was the average birth weight for the day? Round to two decimal places. ( 6.9+ 3.7+ 7.7+6.6+7.3+5.5+9.9+7.0+5.5+7.7) = 67.8/10 = 6.78 lbs 2. There are five health record analysts in the HIM department where you are working. Their salaries are: $13.87, $14.02, $15.56, $15.75 and $16.32. What is the average salary for the health record analysts? Round to two decimal places. ( $13.87 + $14.02 + $15.56 + $15.75 + $16.32)/5 = 75.52/5 = $15.10 1. A physician on your staff performed 44 cardiac catheterizations last month. 34 of those treated were male. What is the ratio of male patients to female patients who had cardiac catheterizations? # of females + total cases - male cases + 44-34= 10 # of females is 10 Ratio = # of male patients/ # of females patients = 34/10= 17:5 What is the proportion? Round to one decimal place. 34/ (34+10)= 34/44= 0.77=0.8 2. It was reported in your department meeting that over the past year your hospital decreased the number of employees by four percent. Last year there were 389 people employed; how many fewer employees are there this year? Round to a whole number. =(38900-38400)/ 38900 x 100 = 500/38900 x100 = 1.345%

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Decreased by 1.345% and total employee are 38400 3. Your manager needs to purchase a personal computer for the new receptionist in your department. The usual price is $1,100. The local supply company gives the facility a 13 percent reduction on all items they purchase. What price will your manager pay? 13/100= 0.13 1100x0.13=143 1100-143= $957.00 4. Your beginning salary as an analyst in the HIM department is $14.50 per hour. You are due to receive a 3.4 percent cost-of-living raise in your next paycheck. Your performance evaluation is coming up in one month, and you believe you should get an additional 5 percent increase based on your excellent performance. What should your hourly wage be after your next paycheck, and what do you anticipate it will be after your performance evaluation? Cost of living raise = $14.50 x (3.4/100) = $0.493 Hourly wage after cost of living raise= $14.50 + $0.493 = $14.993 Performance based raise = $14.50 x (5/100) = $0.725 Hourly wage after performance evaluation = $14.993 + $0.725 = $15.718 5. Last year, you purchased equipment in the HIM department for $14,250. You have been told that the equipment you bought has depreciated in value by 20 percent. What is the value of the equipment now? 20/100= .20

14250x.20= 2850 14250-2850= $11,400.00 6.You just scored 40 correct out of a possible 50 on your health information test. What percentage did you earn? = (total points earned/ total points possible)*100 = (40/50)*100= 80% 7. Last year, the number of hospitals in your state decreased from 320 to 240. What is the percentage of decrease? 240/320= 0.75 0.75x100= 75% 25% is the decrease percentage Descriptive Statistics – Chapter 10 1. ___________________ statistics are used to explain data in ways that are manageable and easily understood. c. Descriptive statistics 2. Calculate the mean, median, and mode for the following inpatient’s length of stay. Round to one decimal place. LOS: 4, 5, 3, 1, 2, 5, 5, 6, 1, 2, 18, 3 a. Mean LOS: 4+5+3+1+2+5+5+6+1+2+18+3/12= 4.58 b. Median LOS: 12+½= 6.5= ⅗ c. Mode LOS : 5

d. Which LOS would be considered an Outlier? LOS 18 3. Dr. Needleman’s office tracked the number of upper respiratory infection (URI) patients she saw for eight weeks. The following table lists the number of patients seen each week. What is the median for the following values? Dr. Brown’s URI Patients Week 1 20 Week 2 18 Week 3 27 Week 4 17 Week 5 15 Week 6 9 Week 7 9 Week 8 5 = 15+17/2 = 16 Median is 16 4. The NICU at Community Hospital track the weight of the infants in its care. The values for one day are as follows (round to one decimal place): BABY WEIGHT Baby Girl Turner 4.9 pounds

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Baby Boy Sandoval 5.6 pounds Baby Boy Byrd 3.0 pounds Baby Boy Dorsey (A) 3.6 pounds Baby Boy Dorsey (B) 3.9 pounds Baby Girl Hicks 2.1 pounds Baby Girl McCoy 2.8 pounds Using the above information what is the range? Expressed as a spread: 2.1 to 5.6 Expressed as a single value: 5.6 - 2.1= 3.5 Range is 3.5 5.The physical therapy department in Community Hospital pulled the following sample of patients that received physical therapy for adhesive capsulitis of the shoulder (ICD-10 Diagnosis code M75.0X). The data represents the number of physical therapy hours the patients received before being released. Using the data in the table below, calculate the mean, range, variance, standard deviation, and the median to one decimal place. Patient # of Physical Therapy Days PT days-Mean (X – X –) (PT days-Mean) 2 ( X – X –) 2 1. Patient A 32 –10.9 118.8 2. Patient B 41 –1.9 3.6 3. Patient C 25 –17.9 320.4

4. Patient D 62 19.1 364.8 5. Patient E 71 28.1 789.6 6. Patient F 35 –7.9 62.4 7. Patient G 37 –5.9 34.8 8. Patient H 53 10.1 102.0 9. Patient I 44 1.1 1.2 10 . Patient J 29 -13.9 193.2 a. What is the mean? 73+25+62+71+35+37+53+44+29/10 = 429/10 = 42.9 b. What is the range? 71 -25 = 46 c. What is the variance? 118.81+ 3.61+ 320.41 + 364.81 +789.61 +62.41+ 34.81+102.01+1.21+193.21/10 = 1990.90/10 = 199.09 d. What is the standard deviation? 14.1 e. What is the median? 37+41/2 = 72/2= 39 6. There were 16 babies born at Community Hospital during the first week of July. The following represents the weight of each of the babies. 4.6, 5.8, 5.3, 5.5, 6.0, 8.3, 6.7, 7.7, 9.4, 6.3, 7.2, 8.0, 6.8, 5.9, 10.0, 5.7

a.What weight is found in the 75th percentile? 7.7lbs 16* 75%= 16 x 75/100 = 12th b. What percentile of newborns weighed over 5.9 lbs? 62.5% 5.9lbs= 10/16 x 100% = 62.5 % Use the following table to answer questions 7 and 8. Dr. Miller, a new endocrinologist at the Community Physician’s Clinic, acquired 10 new diabetic patients during her first month of practice. Their A1C results are listed below. New patients seen by Dr. Sherman September 20XX Patient Number A1C result Patient’s weight 1 5.4 154 2 5.6 167 3 6.7 202 4 6.8 219 5 6.2 198 6 11.7 245 7 10.9 256 8 6.5 195 9 7.8 215 10 9.5 222 7.She would like to offer a weight-loss clinic to the patients who are above the 40th percentile of the results. At which A1C would patients be invited to attend the weight loss clinic?

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= 40 x 10 / 100= (400/100) = 4 6.7 8. What is the range of weights of her new patients? 256-154= 102 9. Fifteen patients have the following LOS: 1, 4, 7, 2, 3, 17, 5, 3, 12, 7, 6, 5, 14, 7, and 2. Calculate the mean, median, and mode. Round the mean and median to one decimal place. Mean= 1+2+2+3+3+4+5+5+6+7+7+7+12+14+17/15 = 95/15 = 6.3 Median = (15+½)th = (16/2)th = 8th = 5 Mode= 7 Use the following scenario to answer questions 10 and 11. The office manager at Community Physician’s Clinic received a complaint that a patient had to wait a very long time before being called into an exam room. She wants to investigate what the mean and median wait time is at the clinic. She wishes to use the median to determine the wait times. She surveyed the patients in the clinic on one day. (In minutes): 10, 22, 11, 7, 9, 14, 12, 18, 24, 8, 7, 9, 15, 12, 13, 15 10. What is the mean wait time at the clinic? Round to a whole number. 10+22+11+7+9+14+12+18+24+8+7+9+15+12/14 = 178/14 =89/7 = 12.714 = 12.7 = 13 minutes 11. What is the median wait time at the clinic? 11+12/2 = 23/2 = 11.5 minutes

Mathematical Review - Chapter 10

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