This document provides an overview of key mathematical concepts used in calculating and reporting healthcare statistics, including fractions, decimals, percentages, ratios, proportions, rates, and averages. Fractions, decimals, and percentages are explained, along with how to convert between them. Methods for rounding numbers and calculating ratios, proportions, rates, and averages are also outlined.

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Calculating and Reporting
Healthcare Statistics, Sixth Edition
Chapter 2:
Mathematics Review

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Learning Objectives
• Calculate using decimals, ratios, proportions, rates, and
percentages
• Differentiate between a numerator and denominator
• Perform rounding whole numbers and decimals
• Determine the proper conversion of fractions and decimals
to percentages
• Compute the average or mean
2

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Fractions
• A fraction is one or more parts of the whole
• The top number is called the numerator
• The bottom number is called the denominator
• Example:
3
5
• 3 is the numerator
• 5 is the denominator

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Quotient
• The number obtained by dividing the numerator of
a fraction by the denominator
• May be expressed in decimals
• Example:
3
5
= 0.6
• 0.6 is a quotient

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Decimal Fractions
• Simply referred to as decimals
• In the decimal number 14.37, the digits 3 and 7 are
called decimal digits
• All digits to the right of the decimal point are called
decimal digits
• The decimal point is merely a way of separating the
whole number part (14) from the fraction part (.37)
• 14.37 simply means there are 14 whole parts in this
value plus .37 fraction parts
• The decimal .5 is usually written as 0.5 in order to call
attention to the decimal point

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Decimal Places

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Rounding Whole Numbers
• A process of approximating a number
• One way of approximating is to round the number
to the nearest 10, 100, etc.

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Rounding to the Nearest Ten
• For example the number 31 is between 30 and 40, but
it is closer to 30
• 37 is between 30 and 40, but it is closer to 40
• If you are asked to round to the nearest ten, 31 is
rounded to 30 and 37 is rounded to 40
• If a number is exactly between the two multiples of ten,
then the rule of thumb is to round up
• 35 would be rounded up to 40
• Anything between 35 and 39 would be rounded up to
40
• Anything between 34 and 31 would be rounded down
to 30

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Rounding to The Nearest Hundred
• Refers to rounding numbers that fall between
multiples of 100
• 327 is between 300 and 400
• The 2 in the tens place indicates we should round down to 300
• 7,868 is between 7,800 and 7,900
• The 6 in the tens place indicates we should round up to 7,900
• When the last two numbers are exactly between two
multiples of 100, the rule of thumb is to round up; 350
would be rounded to 400.

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Rounding to The Nearest Thousand
• Refers to rounding numbers that fall between
multiples of 1,000
• We must look at the last three digits.
• If the last three digits are 449 or less, then the
number is rounded down; in the number 7,337, the
337 indicates that 7,337 should be rounded down
to 7,000

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Rounding to The Nearest Thousand
(continued)
• The number 7,868 falls between 7,800 and 7,900.
In this case, the 868 indicates that 7,868 should be
rounded up to 7,900
• If the last three numbers are exactly between two
multiples of 1,000, the rule of thumb is to round
up; 7,500 would be rounded up to 8,000.

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Rounding Decimals
• Each healthcare facility has its own policy on the
number of decimal places used in computing and
reporting percentages
• Most healthcare statistics are reported as decimals.
• If the digit in the first decimal place is less than 5,
leave the whole number as it is
• If the digit is 5 or more, round up to the next whole
number
• For example: 14.4 = 14; 14.5 = 15

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Rounding Decimals (continued)
• If you need to “carry out” the number, round based
on the number one decimal place to the right of
the decimal places needed
• For example, when rounding to one decimal place:
14.46... = 14.5; 14.13... = 14.1
• Notice in 14.46..., we rounded up to .5 because the 6 in
.46 is greater than 5
• In 14.13..., notice that the 3 in .13 is not over 5;
therefore, we rounded down, to .1

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Percentages
• The ratio of a part to the whole is often expressed
as a percentage
• A percentage is a fraction expressed in hundredths
• For example: 34% means 34/100
• This is a useful way to make fair comparisons
• Not all percentages are converted to whole
numbers
• For example: 1/8 = 0.125 = 12.5%

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Changing a Fraction to a Percentage
• Divide the numerator by the denominator and
multiply by 100
• The term ‘percent’ may be interpreted as ‘per one
hundred’
• For example: ½
• Divide 1 by 2 which equals 0.5
• Then multiply by 100, because you need to convert this
‘per one hundred’
• 1/2= 0.5 x 100 = 50%

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Changing a Decimal to a Percentage
• Multiply the decimal by 100
• For example: 0.29
• 0.29 × 100 = 29%

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Changing a Percentage to a Fraction
• Eliminate the percent sign and multiply the number
by 1/100
• For example: 5%
• 5% = 5 × 1/100 = 5/100
• Fractions are usually converted to their simplest
form
• In the example of 5 percent, both 5 and 100 can be
divided by 5, which would result in a fraction of 1/20

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Changing a Percentage to a Decimal
• Eliminate the percent sign and place decimal point
two places to the left
• For example: 76% = 0.76
• If the percentage is only one digit, place a 0 in front
of the number and place the decimal point in front
of the 0
• For example: 4% = 0.04

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Calculating Ratio
• A ratio expresses the relationship of one quantity to
another.
• Ratio is calculated by dividing one quantity by another
• The number can be greater than 1 or less than 1
• For example, if seven men and five women were in a group, the
ratio of men to women would be 7/5 or this may be written as 7:5
and is verbalized as 7 to 5
• Ratios should be simplified to simplest form.
• The numbers 7 and 5 have no common factors, so you cannot
simplify the ratio
• However, suppose there are 6 men and 10 women in a group
• The ratio is now 6:10
• The numbers in this ratio do have a common factor of 2, so you can
simplify this ratio by dividing each number by 2.
• The ratio in this case would be 3:5

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Proportion
• A proportion is a ratio in which x is a portion of the
whole, x + y
• In a proportion, the numerator is always included in
the denominator:
• For example, if two women out of a group of ten over
the age of 50 have had cancer, where x = 2 (women who
have cancer); and y = 8 (women who do not have
cancer); the calculation would be 2/(2 + 8) = 0.2
• The proportion of women that have cancer is 0.2

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Rate
• A rate is a ratio in which there is a distinct
relationship between numerator and denominator
and the denominator often implies a large base
population
• A measure of time is often an intrinsic part of the
denominator
• Careful attention should be given to rates and
percentages
• Errors can occur due to misplaced decimal points
• The term rate is often used loosely to refer to rate,
proportion, percentage, and ratio

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Calculating Rate
• The basic rule of thumb for calculating rate is to
indicate the number of times that something
actually happened in relation to the number of
times that something could have happened
(actual/potential)
• Formula
• Rate = Part/Base or R = P/B

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Averages
• An average is the value obtained by dividing the
sum of a set of numbers by the number of values
• Also referred to as the mean
• For example:
• If a student took six tests in a particular class and the
scores are 82, 78, 94, 56, 91, and 85
• Added together these equal 486
• Divide 486 by 6 = 81
• The student’s average score is 81