C. Reducing fractions to lowest terms

1. To reduce a fraction to lowest terms, divide both the numerator and denominator by the largest multiple common to both terms. The fraction will maintain its value but change its form.
   
   a. Example: 15/24 is reduced to 5/8 by dividing both numerator and denominator by 3:
   
   

D. Five rules for calculating with fractions

1. Understand the impact of multiplying or dividing the numerator and/or denominator by a whole number.
   
   Example:        4/8
   
   
   
2. Convert mixed numbers or whole numbers to improper fractions before performing calculations with other fractions.
   
   a. Example:        2 7/8 = 23/8
   
3. When adding or subtracting fractions, make sure all fractions have a common denominator (i.e., a number into which all denominators may be divided an even number of times).
   
   a. Example:         3/4, 5/8, 1/2 may be written as 6/8, 5/8, 4/8
   
4. Convert answers that are improper fractions back to whole numbers or mixed numbers.
   
   a. Example:         15/3 = 5
   
5. Convert answers to lowest terms
   
   a. Example: 16/32 = 8/16 = 4/8 = 2/4 = 1/2

E. Adding and subtracting fractions

1. First convert all fractions to a common denominator. Then add or subtract the numerators.
   
   a. Example:         1/2 + 5/6 + 3/8 = 12/24 + 20/24 + 9/24 = 41/24 = 1 17/24
   
   b. Example:         13/32 – 3/8 = 13/32 – 12/32 = 1/32

F. Multiplying fractions

1. Unlike addition and subtraction, multiplying fractions does not require common denominators. Multiply numerators by numerators and denominators by denominators.
   
   a. Example:         9 2/7 × 3/4 = 65/7 × 3/4 = 195/28 = 6 27/28

G. Dividing fractions

1. Invert the divisor and multiply the fractions.
   
   a. Example:         11/12 ÷ 1/6 = 11/12 × 6/1 = 66/12 = 5 1/2
   
   b. Example:         10 3/5 ÷ 2 1/10 = 53/5 ÷ 21/10 = 53/5 × 10/21 = 530/105 = 5 5/105 = 5 1/21

II. Decimals

A. Converting decimals to fractions

1. Decimal fractions are fractions with denominators of 10 and/or multiples of 10.
   
   a. A decimal number with one digit to the right of the decimal point is expressed in “tenths.”
   
   
   
   (1) Example:         0.7 = 7/10
   
   
   b. A decimal number with two digits to the right of the decimal point is expressed as “hundredths.”
   
   
   
   (1) Example:         0.27 = 27/100
   
   
   c. Follow the same rule as more digits are added to the right of the decimal point.
   
   
   
   (1) Example:         0.0365 = 365/10,000

B. Converting fractions to decimals

1. To convert common fractions to decimal fractions, divide the numerator by the denominator.
   
   a. Example:         3/4 = 0.75
   
   b. Example:         1 5/8 = 13/8 = 1.625

C. Adding, subtracting, multiplying, and dividing decimals

1. When adding, subtracting, multiplying, and dividing decimals and common fractions, convert all terms to the same system before performing the calculation.
   
   a. Example:         25/100 + 1.005 = 0.25 + 1.005 = 1.255

III. Roman Numerals

A. Primary Roman numeral units

SS = 1/2

I or i = 1

V = 5

X = 10

L = 50

C = 100

D = 500

M = 1000

B. Eight rules for using Roman numerals

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