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:

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

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

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 :

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:

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

Division example:

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:

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:

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:

Answers to Module 1 Practice Problems

Problem Type 1 –Working with Decimal Numbers

Adding Decimal Numbers

Subtracting Decimal Numbers

Multiplying Decimal Numbers

Don't forget your rounding rules.

Dividing Decimal Numbers

Problem Type 2 – Working with Fractions

Adding Fractions

Subtracting Fractions

Multiplying Fractions

Dividing Fractions