Foundations, College Math WGU
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Order of Operations
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P.E.M.D.A.S.
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What does PEMDAS stand for?
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Please Excuse My Dear Aunt Sally, or 1. Parentheses; 2. Exponents (and square roots); 3. Multiplication, Division; 4. Addition, Subtraction.
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Greatest Common Factor vs. Lowest common Multiple/Denominator
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GCF The COMMON FACTOR that repeats the GREATEST number of times.. Use the GREATEST number of repetitions IN COMMON. Multiply. Eg: 40 = 2x2x2 x5 20 = 2x2 x5 GCF = 2x2 LCM (compare multiples of denominators or...) The combination of all the factors for all the numbers. Only represent each number once. For repeating numbers, represent the largest number of repetitions in any one factorization. Eg: 15 = 3x5 18 = 3x3x2 LCM = 3x3x2x5
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Mixed Number to Improper Fraction
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Whole Number x Denominator + Numerator is the new Numerator. Eg: 8 1/4 8x4+1 / 4
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Multiply Fractions
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Multiply Across Eg: 2/3 x 2/3 = 2x2/3x3 Shortcut: Diagonal numbers can cancel each other out. Eg:10/1 x 5/10 = 5
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Divide Fractions
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Cross Multiply or Multiply first fraction by the reciprocal of the second. Eg: 2/3 div 3/4 2/3 x 4/3
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Blank Card
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Blank Card
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What is the result when multiplying a Negative and a Positive?
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Negative
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What is the result when multiplying a negative and a negative?
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Positive
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What is the result when dividing a negative and a positive?
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Negative
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What is the result when dividing a negative and a negative?
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Positive
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Anything / 0 =
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Undefined or No Answer
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Add or subtract fractions
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1. Convert all to lowest common denominator 2. Add or subtract numerators
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Step 1 in deciding what type of number it is
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Simplify Eg: a fraction might not be a whole number, but it might be if simplified
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Natural Numbers
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1,2,3,4.... (DOES NOT INCLUDE ZERO) (No negatives, decimals, fractions)
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Whole Numbers
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0,1,2,3,4.... (No negatives, decimals, fractions)
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Integers
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...-3,-2,-1,0,1,2,3... (no decimals, fractions)
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Rational Numbers
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All Integers plus fractions, and decimals as long as they are repeating or terminating.
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Irrational Numbers
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1.Decimals that are non-terminating or non-repeating 2.Fractions with Zero as denominator 3.Square roots that have no square
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Real Numbers
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All rational and irrational numbers (which includes all natural, whole, integers).
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Imaginary Numbers
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Square root that when squared is a negative. EG: Square root of negative 1. This wasn't in course materials.
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Additive Inverses or Opposites vs. Negative Reciprocal
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Additive Inverse: -6 and +6 Negative Reciprocal : 2/1 vs -1/2
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Constant
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A lone number in an algebraic equation. (Not a co-efficient or a variable.)
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Coefficient
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the number right in front of the variable (to be multiplied with the variable) in an algebraic equation.
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Absolute Value
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Distance from Zero. Therefore always positive.
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Write a Ratio
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1:10 or 1/10
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Convert % to decimal
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Move decimal two places to the left. (Because 12% = 12/100 or .12)
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Convert % to fraction. Include percent with decimal.
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12% = 12/100 12.5% = 125/1000
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Convert fraction to %
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1. 7/8 = P/100 2. Crossmultiply: 8P = 700 3. Continue to solve for P
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Percent Problems - Fraction Method
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Part/Whole = %/100 or Is/Of = %/100
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Percent Problems - Sentence Method
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1. What percent of 20 is 30? ;;; y% x 20 =30 2. What is 35% of 80? ;;; y = .35 x 80 3. 45% of what is 9? ;;; .45 x y = 9 DANGER! MUST REMEMBER TO CONVERT DECIMAL ANSWER BACK TO PERCENT. BY MOVING THE DECIMAL.
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How to solve an absolute value equasion
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Has two solutions. Run positive and negative scenarios. Eg: |2x-5|= 9 and |2x-5|= -9
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|anything| = any negative number
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Empty Set or No Answer
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How to write an ordered pair
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(x,y) Include parenthesis
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Slope
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Rise/Run or y1+y2/x1+x2
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First step to graph this: y=-2x
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Make up numbers for x
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What kind of line has a negative reciprocal slope?
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Perpendicular Line
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What is a negative reciprocal?
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2/1 vs -1/2
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Positive vs. Negative slope
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"Read" from left to right Positive: / Negative:
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Y Intercept written form X Intercept written form
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(0,y) (x,0)
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Slope-Intercept Form Equation
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y=mx+b m = slope even if the rest of the equation not solved. b = y intercept If there is no b, b is zero If there is no x or y, they are zero
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Slope of Horizontal and Vertical Lines
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Horizontal: 0 Vertical: "undefined" since anything/0 = "undefined"
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Slope and X-Intercept of x = 3
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(3,0) Vertical Line 3/0 = "undefined" slope
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Slope and y-intercept of y=3
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(0,3) Horizontal Line Slope Zero
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Point-Slope Form Equation
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y-y1 = m(x-x1) m = slope line passes through y1 and x1
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Standard Form Equation for finding slope
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Ax+By=C Slope = -A/B X Intercept = (C/A, 0) Y Intercept = (0, C/B)
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Two ways to notate an angle
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;J or ;IJK (actual angle sign slightly different) Can be just the virtex or points surround virtex
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Measurement of a straight angle
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180 degrees
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Measurement of a right angle
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90 degrees
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Measurement of Obtuse Angle
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Between 90 and 180 degrees
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Measurement of Acute angle
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Less than 90 degrees
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Circumference of a square, triangle, circle
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Square = sum of sides Triangle = sum of sides Circle = 3.14 x diameter or 3.14 x 2radius
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Area of a square, triangle, circle
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Square = length x height Triangle = 1/2 x base x height Circle = 3.14 x radius2(squared)
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Volume of Square, Triangle, Circle
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Square = length x height x width Triangle = no method given Circle =3.14 x radius2(squared) x height
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Circumference or Area "in terms of Phi" or "without rounding"
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There is a Phi in left in the answer (The symbol is in the answer and the 3.14 hasn't been calculated in.)
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Circumference, area, and volume of a square
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Circumference = sum of sides Area = length x height Volume = length x height x width
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Circumference, area and volume of a triangle
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Circumference = sum of sides Area = 1/2 x base x height Volume = no method given
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Circumference, Area, and Volume of a Circle
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Circumference = 3.14 x diameter or 3.14 x 2radius Area = 3.14 x radius2(squared) Volume = 3.13 x radius2(squared) x height
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Congruent Triangles
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Same size and shape.
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Similar Triangles
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Same degrees of angles, but different size
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Corresponding sides of a triangle
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In similar triangles, the corresponding sides are opposite the corresponding angles
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Find missing figures for corresponding sides of similar triangles
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Ratio of what you know equated to ratio including variable eg: 1. 20/10 = x/8 2. Crossmultiply. 10x = 160 3. Solve for x
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P verses P1 (superscript)
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P = the pre-image P1 = the image P1 is after the image has been changed
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Define Rotational Symmetry
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If you rotate the image around a central point 180 degrees or less, the image will be superimposed on itself.
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Figure Rotational Symmetry (Degree of rotation needed for image to superimpose on itself)
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360degrees/# of lines of symmetry
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Define Reflectional Symmetry
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Can be mirror image of itself on two sides of a line of symmetry
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What are the measures of central tendency?
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Average, Mean, Weighted Mean, Median, Mode
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Find Mean or Average
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Sum of items / number of items
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Find weighted mean
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instance x amount + instance x amount /number of instances
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Find median
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arrange values in order, use middle number or the average of the two middle numbers
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Mode
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the number or numbers found most often in a set of numbers
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Calculate number of possible combinations with units that cannot be repeated, like people sitting or numbers drawn from a hat, verses units that can be repeated like landing on a color on a colorwheel
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Non repeating units: 5x4x3x2x1 Repeating units: 5x5x5x5x5
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Number of letters in the alphabet
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26
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Number of single digits
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10 (0-9)
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Probability Formula
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Events/Sample Space or Root Beers/Total Sodas or Chances for the desired outcome/Number of possible outcomes
