Pharmacology: Fractions, Decimals, and Percents/ Dosage Calculations

mixed number

An improper fraction can be written as a _____, which is a whole number plus the fractional remainder. That id, divide the denom. of the improper fraction into the num. and placing any remainder over the original denom.. If there is no remainder, the improper fraction is a whole number. Examples 5/5 = 1, 7/5 = 1 2/5, 24/8 = 3. fractions are generally written in their reduced or their lowest terms Example 6/12 reduces to 1/2 by dividing both num. and denom. by 6

Decimal (s)

Any whole number may be divided into tenths (0.1), hundredths (0.01), thousandths (0.001), and so on. These divisions of a number by orders of 10 (10, 100, 1000 etc.) are known as ________ fractions, or _____________. They are another way of expressing fractions. Example: 1/10 = 0.1; 1/100 = 0.01; 1/1000 = 0.001

Multiplying Percents

Change the percent to a decimal (in hundredths) and multiply. Example: 15% of 75 = 15% = 0.15 then 75 x 0.15 (2 decimal places) = 11.25 92 decimal places) 0.2 % of 50 = 0.002 (3 decimal places) = 50 x 0.002 = 0.100 (3 decimal places)

improper fraction

Fractions whos values are equal to or greater than 1 (num. is equal to or greater than the denom,0 are called ______. Examples: 5/5, 7/5, 11/6, 15/8

proper fraction

Fractions whos values are less than 1 (num. is smaller than the denom.) are called ______. Examples: 1/4, 2/3, 7/8, 9/10

Dividing a fraction by a whole number (divisor)

Pace the divisor over 1 , invert it , and then multiply as before. Example 3/4 divided by 4 = 3/4 divided by 4/1 = 3/4 x 1/4 = 3/16

fraction

Part of a whole. A _____ is composed of two numbers, a numerator and a denominator.

To change a decimal to a fraction

Place the decimal number over the order of 10 (10, 100, 1000, etc.) that corresponds to the last place of the decimal and reduce to lowest terms. Example 0.5 (tenths) = 5/10 = 1/2; 0.25 (hundredths) = 25/100 = 1/4; 0.005 (thousandths) = 5/1000 = 1/200

Multiplying a whole number by a fraction

Place the whole number over a denominator of 1 and then multiply nums. and denoms. example 10 x 1/2 = 10/1 x 1/2 = 10/2 = 5

To change a fraction to a decimal

Simply divide the num. by the denom. Note that you may need to add zeros after the decimal point in the dividend. Example 1/4 = 1 divided by 4 = 0.25

denominator

The ____ is the bottom of a fraction. It indicates how many parts something has been divided into

numerator

The ______ is the top of a fraction. It indicates how many parts are being referred to

Solving for an unknown number of the proportion

There are 10 milligrams (mg) of drug per milliliter (ml) of solution. How many milliliters must be administered in order to provide 65 mg of drug? 10 mg:1ml (known) = 65 mg:X ml (unknown) 10X = 65 mg (divide both sides by 10 X = 6.5 mg Remember the smaller known ratio is put to the LEFT of the equal sign and the unknown ratio is put to the RIGHT of the equal sign. Solve for X by multiplying the means and the extreme

Dividing decimals

When _______. move the decimal place in the divisor to the far right and then move the decimal place in the number being divided by the same number of places. Example: 25 divided by 0.05 (2 places) so = 5 and 25 = 2500; then, 2500 divided by 5 = 500 0.010 divide by 0.5 (1 place) so = 5 and 0.010 = 0.10; then 0.10 divided by 5 = 0.02

percents

___ means per hundred. So, ______ are decimal fractions with denoms. of 100. Example: 10% = 10/100 = 0.10 25% = 25/100 = 0.25

proportion

____ is a mathematical equation that expresses the equality between two ratios. Example 25:5 = 50:10 The first (25) and the last term (10) are called the extremes. The second (5) and third term (50) are called the means. The product (multiplication) of the extremes must equal the products of the means 25:5 = 50:10 25x 10 = 5 x 50 250 = 250

ratio

_____ is the relationship of one number to another expressed by whole numbers (1:5) or as a fraction (1/5). The lowest form of the ratio is determined by dividing the smaller number into the larger number. In this example the ratio would be 5:1

Reducing fractions to their Lowest Terms

______ by diving the num. and denom. by the largest number that will divide into both of them evenly. Examples: 15/20 Divided by 5/5 = 3/4, 35/49 divide by 7/7 = 5/7

Dividing fractions

______ it is similar to multiplying fractions. First you must invert the division (divisor) before multiplying the nums. together and the denoms. together. Example 2/3 divided by 3/4 = 2/3 x 4/3 = 8/9

Multiplying fractions

_______ by nums. together and the denoms. together and reducing to lowest terms. Examples 2/3 x 3/4 = 6/12 = 1/2. if the fraction involve large numbers, reduce the numbers by dividing any num. and any denom. by the same number.

Multiplying decimals

_______ is similar to multiplying whole numbers except for the placement of the decimal point. After multiplying the two decimal numbers, add the total number of decimal places (places to the right of each decimal point) and count off the total number of decimal places in the answer (product). Count from right to left, and put the decimal point in front of the last number you count. Example 1.25 (e decimal places x 0.25 (2 decimal places) = 0.3125 (4 decimal places). When an answer has fewer numbers than total decimal places, add zeros as placeholders to make up the difference. Example: 0.5 (1 decimal place ) x 0.1 (1 decimal place) = 0.05 (2 decimal places)