1. Calculating & Reporting Healthcare Statistics
Second Edition
Chapter 2
Mathematics Review

2. Mathematics Review 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
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3. Mathematics Review The quotient
It is the number you get when you divide the numerator by the denominator
This number may be expressed in decimals
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4. Mathematics Review 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 parts.
The decimal .5 is usually written as 0.5 in order to call attention to the decimal point
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5. Mathematics Review Rounding Whole Numbers Rounding to the Nearest Ten
A process of approximating a number
One way of approximating is to round the number to the nearest 10, 100, and so on
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
So when 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 to 40
Anything between 34 and 31 would be rounded down to 30
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6. Mathematics Review Rounding to the Nearest Hundred
327 is between 300 and 400
The 2 in the tens place, indicates we should round down to 300
7878 is between 7800 and 7900
The second 7 (in the tens place) indicates that we should round up so 7878 is near to 7900
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7. Mathematics Review 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; 17.6 = 18
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8. Mathematics Review Rounding Decimals
If you need to “carry out” the number to one decimal place, the basic rule is to go up two and down one
For example, = 14.5; = 14.1
Notice in – we went out two decimal places to .46, then round down 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 do not round up, but rather keep the .1
If you are required to carry the decimal points out two places, the division process then should be carried out to one more place in the quotient and rounded back
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9. Mathematics Review Percentage as a Type of Ratio
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 = .125 = 12.5%
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10. Mathematics Review Changing a fraction to a percentage For example: ½
Divide the numerator by the denominator
Divide 1 by 2 which equals 0.5
Then multiply by 100, because you need to convert this to hundredths
1/2 converts to 50%
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11. Mathematics Review Changing a decimal to a percentage
For example: 0.29
Multiply the decimal by 100
0.29 x 100 = 29%
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12. Mathematics Review Changing a percentage to a fraction
Eliminate the percent sign and multiply the number by 1/100
For example: 5%
Multiply 5 x 1/100 = 5/100
Convert the fraction to its simplest form
Both 5 and 100 can be divided by 5
5 divided by 5 = 1
100 divided by 5 = 20
5/100 = 1/20
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13. Mathematics Review Changing a percentage to a decimal
Eliminate the percent sign and place a decimal point two places to the left
If the percentage is only one digit, place a 0 in front of it and place the decimal point in front of the 0
76% = .76
4% = .04
104% = 1.04
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14. Mathematics Review Calculating Ratio
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
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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15. Mathematics Review Proportion as a Type of Ratio
A particular type of ratio
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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16. Mathematics Review Rate as Type of Ratio
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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17. Mathematics Review 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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18. Mathematics Review Average
The values obtained by dividing the sum of a set of numbers by the number of values
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