Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Transcript

2.2 and 2.3 More on arithmetic Properties for addition Identity Property: There is a unique real number 0 such that for every real number a a + 0 = a and 0 + a = a Prop. Of Opposites: For every real number a, there is a unique real number –a such that a + (-a) = 0 and (-a) + a = 0 Property of the Opposite of a Sum: For all real numbers a and b -(a + b) = (-a) + (-b) Mishaps • -4 + -4 • 4 - (-4) • -(-4) + 4 • -(-4) – 4 • -(4 + 4) How would you rewrite using the communitive property? 4-3 200-(-300) Subtraction is not communitive…you must convert to addition by using the property of opposites!!! What would be a great way to use Associative and Communitive properties to do these mentally? -16 + (-9) + 8 + 25 3.7 + 4.2 –x + y +6.3 + 12.8 -[24 + (-a)] + [-(-2 + a)] Example • A submarine descended to a level 230 m below the surface of the ocean. Later, it ascended 95 m and then dove 120 m. What was the new depth of the submarine? SAT score break down for 1997 and 1998 Year Male Female Male Female 1997 507 503 530 494 1998 509 502 531 496 Verbal Math Organize Data for the Verbal Portion 1997 1998 Male 507 509 Female 503 502 Organize Data for the Math Portion 1997 1998 Male 530 531 Female 494 496 Notice that when we compare, they have the same format!!! Compare the overall SAT scores for the years 1997-1998 between girls and boys. Organized Data for the Verbal Portion 1997 1998 Male 507 509 Female 503 502 Organized Data for the Math Portion 1997 1998 Male 530 531 Female 494 496 Totals 1997 1998 Male Female What are some things that need to be true in order to combine data? Matrix: • Table of numbers without the headers. 1997 1998 Male 507 509 Female 503 502 507 509 503 502 • Usually represented with capital letters. 507 509 A 503 502 • Classified by its dimensions: rows x columns (m x n) Find two matrices comparing Matinee and Evening. Also determine the “total” matrix. Theater Children Adult Children Adult A 198 350 54 439 B 201 375 58 386 Matinee Evening