Skip to Main Content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

Clinical Calculations: Module 1: Review of Basic Mathematics

Review of Basic Mathematics

Module 1 - Review of Basic Mathematics

 

What’s in this module?

This module is a quick review of the math skills you will need in clinical calculations.  You have done all these problem types in the past, either in college or high school.  No advanced math is required.

Summary of problem types in this module

You’ll be working with decimals and fractions.  The operations you’ll be performing are addition, subtraction, multiplication, and division.

Here’s a quick review of some basic math terminology:

 

Image of the equation 7 divided by 2. The 7 is labeled as the dividend. The 2 is labeled as the divisor. The answer is 3 with a remainder of 1. The 3 is labeled as the quotient.

https://www.basic-math-explained.com/images/math-terms-divi1.jpg      Retrieved 8/15/2019

 

The image of the fraction 4 over 7. The 4 is labeld as the numerator. The 7 is labeled as the denominator.

https://www.basic-math-explained.com/images/math-terms-frac.jpg   Retrieved 8/15/2019

 

Image illustrating Fraction Operations: (1) adding or subtracting fractions with common denominators, (2) adding or subtracting fractions with different denominators, (3) multiplying fractions, (4) dividing fractions.

https://i.ebayimg.com/images/i/151041134054-0-1/s-l1000.jpg     Retrieved 8/15/2019

 

Rounding rules to know

You need to know the rounding rule for numbers less than one ( <1 ), numbers greater than one ( >1 ), trailing zeros, and leading zeros:

  1. If the answer is less than one (1), take the math out three (3) places past the decimal point (the thousandth position) and round to two (2) places past the decimal point (the hundredth position).
  2. If the answer is greater than one (1), take the math out two (2) places past the decimal point (the hundredth position) and round to one (1) place past the decimal point (the tenth position).
  3. Do not include trailing zeros. (Ex: 12.0 mL would simply be expressed as 12 mL and 0.40 mg would be expressed as 0.4 mg)
  4. Always use a leading zero for numbers less than one. (Ex: .25 mL should be expressed as 0.25 mL)

Please see the Resources tab for all your rounding rules.  The equivalents you need to know are also in the Resources section.

 

Problem Type 1 – Working with Decimal Numbers

What’s important when you’re working with decimals?  You must keep track of the decimal places to have the correct number of places in your answer.  Many clinical calculations errors are decimal place errors.

Multiplication example :

The equation is 5.23 times 2.1. When you work out the problem, you get 10.98 which rounds to 11.

Your final answer is 11.  Why 11?  For answers greater than (>) 1, you are to take the math out to two places past the decimal point and round to one place past the decimal point. In this case, the second place past the decimal point is an 8. Therefore you are to round the first digit up from 9 to 10, which affects the whole number.

 

Subtraction example:

The equation is 2.3 minus 1.243. When you work out the problem, you get an answer of 1.05 which rounds to 1.1.

Your answer will round to 1.1 using the rounding rule for numbers >1.

 

Division example:

The equation is 5.2 divided by 2.1. When you work out the problem you get an answer of 2.47 which rounds to 2.5.

Your final answer in this problem is 2.5 using the rounding rule for numbers >1.

 

Problem Type 2 – Working with Fractions

In adding and subtracting fractions, use the lowest common denominator to express the fractions.

Addition example:

The equation is one ninth plus two thirds. To work the problem, you have to find the lowest common denominator. That changes the equation to one ninth plus six ninths. When you had the two fractions, you get an answer of seven ninths.

Change 2/3 to 6/9 so that both terms have the same denominator (9).

 

In multiplication, the lowest common denominator is not necessary.  Multiply the numerators and the denominators.  Then reduce your answer to a mixed number (whole number and fraction) if necessary.

Multiplication examples:

The equation is one eighth times three quarters. Multiply one times three in the numerator to get 3 and multiply eight times four to get 32 in the denominator. The answer is 3 over 32. The fraction cannot be reduced.

The equation is 6 over 7 times 1 and two thirds. First change the mixed number to a fraction. The equation becomes 6 over 7 times 5 over 3. That works out to 30 over 21 which converts to 1 and 9 over 21. The 9 over 21 can be further reduced to 3 over 7. The final answer is 1 and three sevenths.

This problem requires changing a mixed number (1 2/3) into a fraction (5/3), then changing the answer to a mixed number and reducing the fraction.

 

Division only involves one change.  Invert the divisor and multiply as you normally would.

Division example:

The equation is 5 over 8 divided by 2 over 3. First, invert 2 over 3 to 3 over 2. The equation then becomes 5 over 8 times 3 over 2. Multiply the numerators then multiply the denominators. The final answer is 15 over 16.

Module 1 Practice Problems

Module 1 Practice Problems

Problem Type 1 –Working with Decimal Numbers

Adding Decimal Numbers

Problem 1: 1.57 plus 0.23

Problem 2: 5.21 plus 1.39

Problem 3: 6.23 plus 0.59

Problem 4: 7.54 plus 6.01

Problem 5: 8.09 plus 0.99

Problem 6: 8.1 plus 3.59

Problem 7: 2.3 plus 6.84

Problem 8: 2.01 plus 9.9

Subtracting Decimal Numbers

Problem 9: 6.54 minus 1.75

Problem 10: 4.58 minus 2.32

Problem 11: 11.02 minus 0.54

Problem 12: 10.9 minus 0.25

Problem 13: 12.01 minus 5.75

Problem 14: 107.5 minus 0.054

Problem 15: 258.1 minus 0.108

Multiplying Decimal Numbers

Problem 16: 256.12 times 0.75

Problem 17: 122.02 times 1.25

Problem 18: 35.9 times 2.2

Problem 19: 175.5 times 0.33

Problem 20: 0.275 times 50

Problem 21: 1.25 times 3.5

Problem 22: 2.12 times 5.6

Problem 23: 0.12 times 0.975

Dividing Decimal Numbers

Problem 24: 225 divided by 2.2

Problem 25: 512 divided by 2.1

Problem 26: 1054.23 divided by 0.75

Problem 27: 0.75 divided by 0.12

Problem 28: 3.85 divided by 0.45

Problem 29: 779.5 divided by 2.85

Problem 20: 419.23 divided by 60.81

Problem 31: 0.99 divided by 1.55

 

Problem Type 2 – Working with Fractions

Adding Fractions

Problem 32: one over two plus three over eight

Problem 33:  1 over 4 plus 2 over 20

Problem 34:  2 over 7 plus 1 over 6

Problem 35:  3 over 5 plus 1 over 3

Problem 36: 1 over 16 plus 3 over 4

Problem 37: 1 over 8 plus 2 over 3

Problem 38: 2 and 1 over 2 plus 3 over 8

Problem 39: 5 and 1 over 4 plus 1 over 3

Subtracting Fractions

Problem 40: 5 and 3 over 4 minus 1 over 7

Problem 41: 1 and 2 over 3 minus 1 over 4

Problem 42: 9 over 10 minus 1 over 2

Problem 43: 5 over 8 minus 1 over 3

Problem 44: 1 over 10 minus 1 over 4

Problem 45: 8 and 2 over 3 minus 1 over 5

Problem 46: 7 over 8 minus 1 over 4

Problem 47: 2 and 1 over 2 minus 1 over 3

 

Multiplying Fractions

Problem 48: 56 over 9 times 1 over 4

Problem 49: 2 over 9 times 3 over 2

Problem 50: 1 and 1 over 3 times 1 over 4

Problem 51: 3 over 4 times 1 over 10

Problem 52: 2 over 3 times 1 over 4

Problem 53: 1 and 1 over 4 times 1 over 6

Problem 54: 2 and 1 over 2 times 1 and 3 over 4

Problem 55: 3 and 1 over 6 times 2 and 1 over 2

Dividing Fractions

Problem 56: 1 and 1 over 2 divided by 1 over 3

Problem 57:  2 over 3 divided by 1 over 8

Problem 58: 5 and 3 over 4 divided by 1 over 2

Problem 59: 9 over 10 divided by 5 over 6

Problem 60: 3 over 8 divided by 9 over 10

Problem 61: 2 and 8 over 13 divided by 1 over 9

Problem 62: 3 over 8 divided by 1 over 2

Problem 63: 2 and 1 over 2 divided by 5 over 8

 

Answers to Practice Problems

Answers to Module 1 Practice Problems

 

Problem Type 1 –Working with Decimal Numbers

Adding Decimal Numbers

Answers to Adding Decimals Practice Problems: Number 1 is 1.8, Number 2 is 6.6, Number 3 is 6.8, Number 4 is 13.6, Number 5 is 9.1, Number 6 is 11.7, Number 7 is 9.1, and Number 8 is 11.9.

Subtracting Decimal Numbers

Answers to Subtracting Decimals Problems: Number 9 is 4.8, Number 10 is 2.3, Number 11 is 10.5, Number 12 is 10.7, Number 13 is 6.3, Number 14 is 107.4, and Number 15 is 258. Remember not to use a trailing zero. Therefore, the answer to Number 15 is a whole number. 

Multiplying Decimal Numbers

Don't forget your rounding rules.

Answers to Multiplying Decimals Problems: Number 16 is 192.1, Number 17 is 152.5, Number 18 is 79, Number 19 is 57.9, Number 20 is 13.8, Number 21 is 4.4, Number 22 is 11.9 and Number 23 is 0.12.

Dividing Decimal Numbers

Answers to Dividing Decimals Problems: Number 24 is 102.3, Number 25 is 243.8, Number 26 is 1405.6, Number 27 is 6.3, Number 28 is 8.6, Number 29 is 273.5, Number 30 is 6.9, and Number 31 is 0.64.

 

Problem Type 2 – Working with Fractions

Adding Fractions

Answers to Adding Fractions Problems: Number 32 is 7 over 8, Number 33 is 7 over 20, Number 34 is 19 over 42, Number 35 is 14 over 15, Number 36 is 13 over 16, Number 37 is 19 over 24, Number 38 is 2 and 7 over 8, and Number 39 is 5 and 7 over 12.

Subtracting Fractions

 Answers to Subtracting Fractions Problems: Number 40 is 5 and 17 over 28,  Number 41 is 1 and 5 over 12, Number 42 is 2 over 5, Number 43 is 7 over 24, Number 44 is 3 over 20, Number 45 is 8 and 7 over 15, Number 46 is 5 over 8, and Number 47 is 2 and 1 over 6.

 

Multiplying Fractions

Answers to Multiplying Fractions Problems: Number 48 is 1 and 5 over 9, Number 49 is 1 over 3, Number 50 is 1 over 3, Number 51 is 3 over 40, Number 52 is 1 over 6, Number 53 is 5 over 24, Number 54 is 4 and 3 over 8, and Number 55 is 7 and 11 over 12.

Dividing Fractions

Answers to Dividing Fractions Problems: Number 56 is 4 and 1 over 2, Number 57 is 5 and 1 over 3, Number 58 is 11 and 1 over 2, Number 59 is 1 and 2 over 25, Number 60 is 5 over 12, Number 61 is 23 and 7 over 13, Number 62 is 3 over 4, and Number 63 is 4.

 

©2021 Georgia Highlands College | ask@highlands.libanswers.com