Soc 303 Math Review

Math Review

Topic	Topic
Fractions	Decimals
Percentages	Rate
Ratio	Proportion
Rounding	Averaging (the Mean again!)
Converting Fractions to Percentages	Converting Decimals to Percentages
Converting Percentages to Fractions	Computing with a Percentage
Converting other Units of Measure	The math in this course is logical!

Fractions

• Fragment
• Part of a whole
• Small part
• Bit or portion
• Designated by placing one number over another number
  • 2/5 or 9/12
• Composed of two pats:
  • Numerator (number above the line)
  • Denominator (number below the line)
• Always reduce the fraction when you can
  • 9/12 = 3/4

Decimals

Decimals are an amount that is less than one

• 1/10 = 0.10
• 1/100 = 0.01
• 1/1000 = 0.001

This is important when we test for significance in statistics

Percentages

• The number of times something occurs every 100 times
• A specific rate followed by the % sign
• A proportion of a whole
• Converting decimal to percentage:
  • multiply the decimal by 100

Rate

• A value or price (think gas price per gallon)
• A unit of something (think birthrate, cost of living, etc.)
• A ratio, proportion, or rank
• Usually expressed as a percentage

Ratio

• Relationship between things
• Relationship between numbers
• Reported as a fraction or numbers side by side
  • 2:10 is actually 2 out of 10 or 1 out of 5
• Can be reduced (as done above)

Proportion

• A relationship of one portion to another
• A relationship to the whole
• A relationship of one thing to another
• A ratio in which the elements in the numerator must be included in the denominator

Averaging: the Mean again!

• Average is the mean, in this class it is the arithmetic mean…it is not the median or mode!
• Computing is easy!
  • Add all the scores (numerator)
  • N = the number of items in the distribution (denominator)
• The equation: where \(\Sigma\) is the sum
  • \(Average=\frac{\Sigma Scores}{N}\)

Rounding

• Rounding approximates the total final number
• Do not round until the very end of the process!
• Carried to indicates what decimal place is used
  • 2 decimal places = 13.01
• In this class: we use two or three decimal places meaning: REPORT THREE PLACES
  • 13.013
• If the answer is to the nearest whole number
  • Round up (if 5 and over) -> 13.5 = 14
  • Round down (if lower than 5) -> 14.3 = 14

Converting Fractions to Percentages

• Divide the numerator by the denominator
• Multiply by 100
• Add a percent sign

60/80 = 0.75 * 100 = 75%

Converting Ratio to Percentage

• Divide the numerator by the denominator
• Multiply the result (quotient) by 100
• Add a percent sign
• To change 1:8 to a percentage

1/8 = 0.125 X 100 = 12.5%

Converting Decimals to Percentages

• Multiply the decimal by 100 (moves decimal point two places to the right)
• Add a percent sign
• Convert 0.75 to a percentage

0.75 * 100 = 75%

Converting Percentages and Fractions

• Remove the percent sign
• Place the percentage number in the numerator
• Place 100 in the denominator
• Convert to the lowest fraction
• Convert 25% to a fraction

25/100 = 1/4

Computing with a Percentage

• Convert the percent to a decimal
• Example 40% of 100 scores

0.40 * 100 = 40

Converting other Units of Measure

• May need to convert metric to U.S. standards
• Data must be analyzed in the same units
• Linear Measures

Unit	Conversion
1 cm	0.0328 foot; 0.3937 inch
1 inch	2.54 cm
1 foot	0.3048 meter
1 meter	1.0936 yd; 3.2808 feet; 39.37 inches
1 mile	1.6094 km
1 km	0.6214 miles

Weights and Liquids

• Weight Measures
  • 1 gm = 0.0022 lb; 0.0353 oz
  • 1 kg = 2.2046 lb
    
  • 1 lb = 0.4536 kg; 45.36 gm
    
  • 1 oz = 28.3495 gm
• Liquid Measures
  • 1 quart = 0.94633 liter
  • 1 liter = 0.2642 gallons; 1.0567 quarts