Rational Numbers - Ms. Cleveland's Math Class



CRCT Overview Math 8 Introduction to Algebra and GeometryReminder: Properties3509158568200A - The Number SystemRational NumbersA rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.The number 8 is a rational number because it can be written as the fraction 8/1.Likewise, 3/4 is a rational number because it can be written as a fraction.Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a fraction.Every whole number is a rational number, because any whole number can be written as a fraction. For example, 4 can be written as 4/1, 65 can be written as 65/1, and 3,867 can be written as 3,867/1.Irrational NumbersAll numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers:π = 3.141592…= 1.414213…228557129238700Although irrational numbers are not often used in daily life, they do exist on the number line. In fact, between 0 and 1 on the number line, there are an infinite number of irrational numbers!Locating square roots on Number line.B - Expressions and EquationsExponents & Square Roots -1739901421130002677795-381000 21774152540000Scientific NotationRatio and Proportional RelationshipsProportion: relationship between two ratios written as an equation34 = 912Ratio: comparison of two or more amounts3 out of 4 3:43 to 434 Unit rate: comparison of two measurements written as a fraction with the denominator equaling one (as in miles per hour or cost per item)$2.00 for 4 pencils Unit rate = $0.50 2.004= x14792345-16700500Data can be placed in table and create ordered pairs for the coordinate plane.CostUnit Rate5.00 for 10.5012.00 for 101.20 3.00 for 10.30Percent: out of 100; to find percent set up a proportion 34= x100 Cross multiply and then solve equation 20% of 60 means .20 times 60 = 12Slope Intercept34427309713900 64135114300002388485-25280400 Standard Form to slope intercept-33909014859000301371012319000256984524447500 EquationsEquations are complete mathematical sentences. The equal sign can be represented by the word IS in a word problem. OF means multiply usually. THAN tells you to switch the order of the numbers in the word problem.Inverses- operations that undo or reverse another operation. Addition/Subtraction Multiplication/Division 342582514541500190500014922500Two step equations: undo Add/Sub first then Mult/Div 9203381599950076835920750075565635000301032915367000Systems349567514097000 Elimination Method (multiplication): Substitution Method: 1213485508000C – Functions44221409715500349811289668Rule—the math operation(s) you have to do to the inputInput or independent variable—number you start with (x)Output or dependent variable – value you get after using the rule (y)Use substitution and order of operation to complete a function table. 14 = x + 9 x=5 Y = 2 + 9 y=11532574530670500395859042481500 Radical Expressions D – GeometryReflection:TranslationRotation1608265292735 358013012128500Angle Relationships Pythagorean Theorem29629105626100044297609080500-28765553086000 Volume457771524193500 E - Statistics and ProbabilityScatter plots: 289115538798500Inequalities Inequalities compare two or more values that are not equal. Numbers to left on the number line are always smaller than those on the right. If you graph numbers on the number line, you can compare their values from least to greatest going left to right. Use the same rules for solving equations.NOTE: multiplying or dividing by a negative number reverses the inequality symbol.- Statistics and ProbabilityIndependent EventsDependent EventsMeasures of Central Tendency ................
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