PCTC Chapter 2: Percentages, ratios and proportions
percent
% by the hundred or in a hundred an example of a part to whole relationship basically has a denominator of 100 may be expressed as a ratio, decimal or fraction EX: 49% = 49:100 = 49/100 = 0.49
conversion using ratios
- changing a ratio to a fraction or vice versa - converting a ratio in to a decimal (turn into a fraction then divide numerator by the denominator) - convert to a percent by changing to a decimal then muliply by 100 and add %
to convert a fraction or decimal number into a percentage
1. divide the numerator by the deniminator to get a decimal number 2. convert the decimal to the percent by multiplying the decimal number by 100 and adding the % sign 3. OR use the simplified multiplication method. This method of converting a decimal to a percent can be accomplished by shifting the decimal points two places to the right. The decimal is the starting point for a percent conversion and can be greater than 100
convert 2:8 to a fraction
2:8 = 2/8 = 1/4
determining the numerical value of a percent What is the value of 68%
68 parts per 100 68:100 as a ratio 68/100 as a fraction 0.68 as a decimal
converting percentages to decimals convert 76% to a decimal
76% = 76/100 = 0.76
ratio
A comparison of two quantities by division used to express a relationship between two numbers usually separated by a colon (:) Expressed verbally as # is to # can have two sets of colons #:#::#:# where :: means = Ex: 3 is to 6 as 6 is to 12
solving percentage problems invloving fractions what is 5 1/4% of 130?
Step 1: Insert into the formula 5 1/4% x 130 =x Step 2: Convert the percent to an improper fraction 21/4% x 130 = x Step 3: convert the percent to an improper fraction and solve for the unknown (x) (21/4 x 1/100) x130 = X (21/400) x (130/1) = x x = 2730/400 =6.825 Step4: convert improper fraction to a mixed number and reduce to lowest terms 6 x 400 = 2400 2730 - 2400 = 300 X = 6 330/400 = 6 33/40 5 1/4% of 130 is 6 33/40
solving percentage problems what percent of 200 is 12?
Step 1: Insert the known values into the equation x%/100 = 12/200 Step 2: solve for the missing value multiply both sides by 100 to isolate x 100/1 x x%/100 = 12/200 x 100/1 x% = 1200/200 Step 3: reduce to lowest terms x% = 1200/200 =12/2 = 6 12 is 6% of 200
using a proportion to solve a practical problem for an unknown a patient weights 150 lbs. The dictor ordered a drug that has a dosage dependent on milligrams (mg) of medication per kilogram of body weight. The pharmacy technician will need to convert pounds (lb) to kilograms using the ratio of 1 kg: 22. pounds
Step 1: convert ratio to a fraction equation 1 kg/2.2 lbs = Y kg/150 lbs Step 2: Cross multiply to solve for the unknown (Y) Y kg x 2.2 = 150 x 1 2.2 Y kg = 150 2.2 Y/ 2.2 = 150/2.2 Y = 68.18 kg
convering a ratio to a percent convert 1:4 to a percent
Step 1: convert the ratio to a fraction 1:4 = 1/4 Step 2: convert the fraction to a decimal 1/4 = 0.25 Step 3: convert the decimal to a percent multiply the decimal by 100 and add the % sign 0.25 x 100 = 25% ratio 1:4 is equal to 25%
Solving percentage problems involving fractions What is 12 1/4% of 275?
Step 1: insert the known values into the equation (12 1/4%)/100 = Z/275 Step 2: convert the percent to an complex fraction 12 1/4% converted to an complex fraction is 49/4 (49/4)/100 =Z/275 Step 3: Cross multiply diagonally to solve for the unknown (Z) (100 x Z) = (49/4) x 275 100Z = (49/4) x (275/1) 100Z = 13475/4 4 x 100Z = (13475/4) x 4 400Z = 13475 400Z/400 = 13475/400 Z = 33.6875 12 1/4% of 275 is 33.6875 or 33.7
Solving percentage problems
can be solved using proportions or this equation: number of parts /total parts of the whole the equation be also be expressed as % needed x total number of parts of the whole = number of parts needed for the % needed
proportion
compares two ratios to one another used in a wide variety of health care applications and everyday math problems EX: 4/6 equals 8/12 or 4:6::8:12 allows to solve for unknown y when three other values are known Set problem up as fractions than cross multiply
convert a percentage to a decimal or fraction
divide the percent by 100 Or move decimal two places to the left Or convert the percentage by removing the % and placing it over 100 and reducing to lowest terms
the number in a ratio refers to
part of one substance as compared to parts of another substance Units (weight, volume or tablets) can vary but the units must be the same for both
percentage
parts per hundred
What are some reasons pharmacy techs need to know percentages?
percent strength of solutions preparing intravenous solutions dispensing ointments labeled with percents
using a proportion to solve for an unknown (Y) 6 mg : 2 mL :: Y mg : 30 mL
step 1: convert proportion to a fraction equation 6 mg/ 2 mL = Ymg/30mL step 2: cross multiply to solve for the unknown (Y) Y mg x 2 = 6 x 30 2Y mg = 180 (2Y mg)/2 = 180/2 Y = 90 mg 6 mg is to 2 mL as 90 mg is to 30 mL
converting a percent to a ratio convert 30% to a ratio
step 1: convert the percent to a fraction and reduce to the lowest terms 30% = 30/100 = 3/10 Step 2: convert the fraction to a ratio 3/10 = 3:10 30% is equal to 3:10
convert percentages to fractions convert 12.5% to a fraction
step 1: decide by 100 12.5/100 step 2: simplifly to lowest terms (12.5/12.5)/(100/12.5) =1/8
converting fractions to percents convert 3/6 to a percent
step 1: divide the numerator by the denominator to get a decimal 3 /6 = 0.5 step 2: Multiple by 100 and add a percent sign 0.5 x 100 = 50 50%
Solving percentage problems invloving decimals what percent of 120 is 55.2?
step 1: insert to known values into the equation x%/100 = 55.2/120 Step 2: Solve for the missing value multiply both sides by 100 to isolate X (100/1)x (x%/100) = (55.2/120) x (100/1) x% = 552/12 X% = 46 Or cross multiply diagonally to solve for the unknown (x) (x% x 120 ) = (100 x 55.2) 120x% = 5520 (120x%/120) = (5520/120) X% = 46 55.2 is 46% of 120
convert a fraction to a ratio convert 8/16 to a ratio
step 1: reduce fraction to lowest terms 8/16 = 1/2 Step 2: convert to a ratio 1/2 = 1:2 8/16 is equal to 1:2
solving percentage problems What is 40% of 75?
step 1: use the formula %/100 = number of parts/ whole 40/100 = Z/75 step 2: solve for the missing value multiple both sides by 75 to isolate Z (75/1)x (40/100) = (z/75) x (75/1) (75x40)/100 = z 3000/100 = z OR cross multiple diagonally to solve for the unknown (Z) (100xZ) = (40 x 75) 100z = 3000 Step 3: simplify the fraction to a whole number Z = 3000/100 =30 40% of 75 is 30 ALternatively Step 1: insert the known values into the equation 40% x 75 = Z Step 2: Solve for the unknown by converting the decimal and multiplying 0.40 x 75 = Z 30 = Z There for 40% of 75 is 30
the word 'of' means what in percentage problems?
to multiply so 40% of 100 would be multiple 40% by 100
What is the best way to handle percents fractions?
treat them as complex fractions. Do not change fraction to decimal because answer may not be as exact when compared to the fraction calculation The problem should be set up in a proportion format to solve for the answer
when dividing fraction the divisor should be converted to a reciprocal fraction and then multiplied true false
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