1. Basic Math Skills

2. Figure 12.1
Place value.

3. Decimals as Fractions
Decimals are fractions with a denominator that is a multiple of 10
The value of the denominator is determined by the number of digits to the right of the decimal point
Examples:
8/10 represents the decimal 0.8
8/100 represents the decimal 0.08
8/1000 is equivalent to the decimal 0.008

4. Using Zero
Zeros placed before or after a decimal number do not change the value of the number
Examples:
00.8 is the same as 0.8, which is the same as .8
0.800 is the same as 0.80, which is the same as 0.8

5. Using Zero (cont.)
Healthcare professionals always place a zero before the decimal point to avoid misreading of a number (a decimal point not preceded by a zero is easily missed)

6. Adding or Subtracting Decimals
Write the numbers vertically and line up the decimal points
Add zeroes as placeholders, if necessary
Add/Subtract from right to left

7. Multiplying Decimals
Process is the same as for whole numbers, with one additional step at the end
Multiply the numbers, ignoring the decimal points
Add the total number of decimal places from the original numbers

8. Multiplying Decimals (cont.)
Place a decimal point that number of places by moving from the right to the left of the answer
If there are not enough numbers for the correct placement of the decimal point, add as many zeroes as necessary

9. Dividing Decimals
Place the dividend, or number to be divided, inside the division bracket
Place the divisor, or number you are dividing by, outside the division bracket
Change the divisor to a whole number by moving the decimal point all the way to the right

10. Dividing Decimals (cont.)
Move the decimal point in the dividend the same number of places to the right as you did for the divisor
Place a decimal point directly above the decimal in the dividend and divide as normal

11. Table 12.2
Roman Numerals

12. Rules for Changing Roman Numerals to Arabic Numerals
Rule 1: Roman numerals are never repeated more than three times in a row
Rule 2: When a Roman numeral is repeated, or when a smaller numeral follows a larger numeral, their values are added together

13. Rules for Changing Roman Numerals to Arabic Numerals (cont.)
Rule 3: When a smaller numeral comes before a larger numeral, the one of lesser value is subtracted from the larger value
Ones (I) may only be subtracted from fives (V) and tens (X).
Tens (X) may only be subtracted from fifties (L) and hundreds (C).
Hundreds (C) may only be subtracted from five hundreds (D) and thousands (M).

14. Rules for Changing Roman Numerals to Arabic Numerals (cont.)
Rule 4: When a numeral of smaller value comes between two numerals of larger value, the subtraction rule is always applied first, then the addition rule

15. Rules for Changing Arabic Numerals to Roman Numerals
Rule 1: Break the number down into segments that have Roman equivalents
Rule 2: For numbers that have no fast and easy equivalent, it is helpful to use a pen and paper to break the number down into manageable sections
Rule 3: Thorough knowledge of how to change Roman numerals into Arabic numerals is required

16. Common Fractions
A common fraction can be expressed as one number that is set on a fraction line above another number
There are four categories of common fractions: proper fractions, improper fractions, simple fractions, and complex fractions

17. Common Fractions (cont.)
Proper fraction—the value of the numerator is smaller than the value of the denominator
Improper fraction—the value of the numerator is larger than the value of the denominator
Simple fraction—cannot be reduced to any lower terms

18. Common Fractions (cont.)
Complex fraction—fraction in which both the numerator and the denominator are themselves fractions

19. Adding and Subtracting Fractions
Fractions that are to be added or subtracted must all have the same denominator
If necessary, convert each fraction to a fraction with the least common denominator
Then, add or subtract the numerators

20. Multiplying Fractions
Multiply the numerators by the numerators
Multiply the denominators by the denominators
Reduce to lowest terms

21. Dividing Fractions Invert the divisor (flip it upside down)
Multiply the two fractions
Multiply the numerators by the numerators
Multiply the denominators by the denominators
Reduce to lowest terms

22. Ratios A ratio expresses the relationship of two numbers
The numbers are separated by a colon (:)
The ratio x:y indicates that for every “x” amount, there is a “y” amount of something else
Ratios can also be rewritten as fractions
x:y = x/y

23. Proportions
A proportion is two or more equivalent ratios or fractions that both represent the same value
For example, if you need 2x of an ingredient in ratio x:y, you will also need 2y; 2x:2y is a proportion of x:y

24. Solving Ratios and Proportions
Ratios and proportions are solved (settled) by cross-multiplication
Once you have set up two ratios or fractions in relationship to each other as a proportion, you can cross-multiply to solve for the unknown (X)
There are two approaches to using cross-multiplication to solve for X