PRAXIS 5001 MATH WITH 100% CORRECT ANSWERS

How to add fractions. -4/9 + -9/10 = -103/90 Rational Numbers Include fractions, integers, mixed numbers, and terminating and repeating decimals. Integers The positive and negative whole numbers and zero Ex: -6, -5, -4, 0, 1, 2, 3, 4, .... Whole Numbers Natural Numbers and zero. Ex: 1, 2, 3, 4, 5, 0.... Natural Numbers Counting Numbers 1, 2, 3, 4, 5, 6, .... Irrational Numbers Real numbers that cannot be written as a ratio of two integers, they are infinite, non repeating decimals. Mixed Number Has a integer part and a fraction part 5 1/2 Exponent Shortcut method to writing repeated multiplication. four squared, 2 would be the exponent. 4 would be the base Exponent Product Rule 4[2] * 4[2] = 4[2+2] Exponent Quotient Rule 4[2]/4[2] = 4[2-2] Rule of Negative Exponents 4[-2]/4[-3] = - 4[3]/4[2] Scientific Notation A convenient method for writing very long numbers. Each exponent equals a zero. Order of Operations Parenthesis, Exponents, Multiplication and Subtraction (Left to Right), Addition and Subtraction (Left to Right) Four Quadrants Quadrant I (Top Right), Quadrant II (Top Left), Quadrant III (Bottom Left), Quadrant IV (Bottom Right) Prime Factors are 1 and itself Composite Any number that is not prime Monomials, Binomials and Trinomials Polynomials Monomials (1x) Binomials (1x + 3) Trinomials (1x + 3 + 4[2]) Axioms Property's of Math Closure For all real numbers a and b, a + b is a unique real number. Commutative Commutative means that the order does not make any difference in the result. Note: Commutative does not hold for subtraction ab = ba Because the numbers can travel back and forth like a commuter. Associative Associative means that the grouping does not make any difference in the result. The grouping has changed (parentheses moved), but the sides are still equal. Ex: (ab)c = a(bc) Inverse Operation The operation that reverses the effect of another operation. Example: Addition and subtraction are inverse operations. Start with 7, then add 3 we get 10, now subtract 3 and we get back to 7. Another Example: Multiplication and division are inverse operations. Start with 6, multiply by 2 we get 12, now divide by 2 and we get back to 6. Algorithms An algorithm is a set of rules for solving a math problem which, if done properly, will give a correct answer each time. Algorithms generally involve repeating a series of steps over and over, as in the borrowing and carrying algorithms and in the long multiplication and division algorithms. Rectangular Arrays array. (ə-rā') Mathematics A rectangular arrangement of quantities in rows and columns, as in a matrix. Numerical data ordered in a linear fashion, by magnitude. Unit Rate or Unit Ratio A ratio with a denominator of one. This can be found by simplifying any ratio to having 1 as a denominator. Rate: 2/1 Ratio 3:5 Expressions •Can only be simplified. For example:◦Order of operations (aka PEMDAS/GEMDAS ◦Reduce fractions ◦Rationalize denominators •Express an idea. Examples:◦Twice a number: 2x ◦3 less than the square of a number Equations •Can be solved. •Make a statement. Examples:◦Twice a number is 26: 2x = 26 ◦3 less than the square of a number is 6: x%5E2+-3+=+6 •Are formed by two expressions separated by an equals sign. Linear Equation Y=MX + B Independent and Dependent Variables •Independent variables - The values that can be changed in a given model or equation. They provide the "input" which is modified by the model to change the "output." •Dependent variables - The values that result from the independent variables. 12 inches equals 1 foot 3ft equals 1 yard 1760 yards equals 1 mile Area of Triangles Triangle Area = ½ × b × h b = base h = vertical height Area of Rectangle/Parallelogram Rectangle Area = w × h w = width h = height Area of a circle Circle Area = π × r2 Circumference = 2 × π × r r = radius Area of a square Square Area = a2 a = length of side Area of a Rectangular Prism Right rectangular prism •Find the area of two sides (LengthHeight)2 sides •Find the area of adjacent sides (WidthHeight)2 sides •Find the area of ends (LengthWidth)2 ends •Add the three areas together to find the surface area •Example: The surface area of a rectangular prism 5 cm long, 3 cm. wide and 2 cm. high = 522 + 322 + 532 = 20 + 12 + 30 = 62 cm2.