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Positive and Negative Numbers Definition Rational Numbers – numbers that can be expressed as one integer a divided by another integer b, where b is not zero You can write a rational number a in the form or in decimal b form Definition • Positive number – a number greater than zero. 0 1 2 3 4 5 6 Definition • Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Definition • Opposite Numbers – numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Definition • Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero. 7 opposite -7 Hint • If you don’t see a negative or positive sign in front of a number it is positive. +9 Inequalities and their Graphs Objective: To write and graph simple inequalities with one variable Inequalities and their Graphs What is a good definition for Inequality? An inequality is a statement that two expressions are not equal 2 3 4 5 6 7 8 Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly < less than > greater than Notice open circles Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly ≤ less than or equal to ≥ greater than or equal to Notice colored in circles Inequalities and their Graphs Let’s work a few together x>3 Notice: when variable is on left side, sign shows direction of solution 3 Inequalities and their Graphs Let’s work a few together x<7 Notice: when variable is on left side, sign shows direction of solution 7 Inequalities and their Graphs Let’s work a few together p £ -2 Notice: when variable is on left side, sign shows direction of solution -2 Color in circle Inequalities and their Graphs x³8 Color in circle Notice: when variable is on left side, sign shows direction of solution 8 Ordering fractions If the DENOMINATOR is the same, look at the NUMERATORS, and put the fractions in order. 1 2 3 4 7 9 9 9 9 9 (if ordered smallest largest) Ordering fractions If the DENOMINATOR is the different, we have a problem that must be dealt with differently. 3 7 4 1 2 6 8 4 3 4 We need to convert our fractions to EQUIVALENT fractions of the same DENOMINATOR. We will come back to this example. Ordering fractions If the DENOMINATOR is different, we have a problem that must be dealt with differently. 4 3 6 9 Here’s an easier example, with just 2 fractions to start us off. Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE. 4 3 6 9 This means that we check to see which numbers are in the 6 times table, and the 9 times table. We need a number that appears in both lists. Homework Page 20-21, #’s 5, 9-19 ODD, 20-21 Page 22-23, #’s 24-44 EVEN, Page 26, #76-77 Page 27, #78-84 EVEN, 85-87