REVIEW OF BASIC MATHEMATICAL RULES
Rules for Signed Numbers Addition Rules: positive + positive = (add) positive Ex: 2 + 1 = 3
negative + negative = (add) negative Ex: –3+ (–5) = –8
negative + positive = (subtract) and Ex: 2 + (–10) = –8 take sign of number with largest Ex: –14 + 16 = 2 absolute value
------------------------------------------------------------------------------------------------------------------- Remember: –(–7) means take the opposite of (–7) = 7 ----------------------------------------------------------------------------------------------------------------- Subtraction Rules: Change all “subtraction” to addition and take the opposite sign of the following number then follow the addition rules.
Ex: –7 – (9) means Ex: –3 – (–10) means –7 + (–9) = -16 –3 + (10) = 7
Ex: –8 + (–9) – (–1) – 2 -change all subtraction signs as indicated above
–8 + (–9) + (1) + (–2) -do addition and subtraction from left to right
–17 + (1) + (–2)
–16 + (–2) = –18
Multiplication/Division Rules: The rules for multiplication and division are the same. positive ( or ) positive = positive Ex: 10 2 = 5 negative ( or ) negative = positive Ex: –4 (–3) = 12 negative ( or ) positive = negative Ex: 18 (–2) –9
Tutoring and Testing Center
Order of Operations: Parenthesis; Exponents; Multiplication or Division from left to right; Addition or Subtraction from left to right
P.E.M.D.A.S.
Ex: -7 + 20 ÷ (-4)(5)- 32 - (-8) + 4(3 – 7) 1. Parenthesis -7 + 20 ÷ (-4)(5) - 32- (-8) + 4(-4) 2. Exponents -7 + 20 ÷ (-4)(5) - 9 - (-8) + 4 3. Division -7 + (-5) (5) - 9 - (-8) + 4 4. Multiplication -7 + (-25) - 9 - (-8) + 4 5. Addition -32 - 9 - (-8) + 4 6. Change subtraction signs -32 + (-9) + (8) + 4 -41 + 8 + 4 -33 + 4 = -29
--------------------------------------------------------------------------------------------------------------------- Percent Equation:
What percent of the total is the part? % T = P
12% of the 200 students enrolled in freshman English earned a grade of “A” in the class. How many students earned an “A”? Ex: 12% of 200 is what - Translate into an equation (“of” means “multiply”; “is” means “equal”) 0.12 x 20 = x - Change % to a decimal 24 = x
Percent Decrease/Increase: Last year student employment jobs paid $7.25 per hour. This year student employment jobs are paying $8.45 per hour. What percent increase was given to student employment jobs?
1. Find the amount of the increase: $8.45 - $7.25 = $1.20
2. Which (hourly pay) total received an increase? The $7.25 per hour got increased.
3. What % of the total was the increase? x 7.25 = 1.20 7.25x = 1.20
25.7 20.1
25.7 25.7 x x = .1655 x = 16.6% increase -------------------------------------------------------------------------------------------------------------------- Place Value: 101 = 10 10–1 = 0.1 102 = 100 10–2 = 0.01 103 = 1000 10–3 = 0.001 104 = 10000 10–4 = 0.0001 -------------------------------------------------------------------------------------------------------------------
Angles: Acute Angles: less than 90 degrees Obtuse Angles: more than 90 degrees Right Angles: 90 degrees Straight Angle: 180 degrees Complementary Angles: Two angles the sum of whose measures is 90 degrees Supplementary Angles: Two angles the sum of whose measures is 180 degrees
Triangles: Triangles: Sum of the interior angles is 180 degrees Isosceles Triangle: Two equal sides; two equal angles Equilateral Triangle: Three equal sides; three equal angles
Right Triangles - Pythagorean Theorem: a2 + b2 = c2, where a and b are the measures of the legs of the triangle and c is the hypotenuse.
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Statistics:
Mean (average) = sum of all values divided by number of values Median = middle value when the values are arranged numerically Mode = the data value that occurs most frequently -------------------------------------------------------------------------------------------------------------------- Probability: P(A) = sizesampletotal Aoffrequencythe