Transcript 2-1
2-1 Integers Do Now Compare. Use <, >, or =. 1. 7____5 2. 32____65 3. 82____28 4. 64____48 2-1 Integers Today’s Objective: (Goal) Learn to compare and order integers and calculate absolute value. 2-1 Integers Whole Numbers are numbers with no decimal or fractional parts (including 0) The whole numbers are the counting numbers and zero: 0, 1, 2, 3, . . . . 2-1 Integers The opposite of a number is the same distance from 0 on a number line, but on the opposite side of 0. Zero is its own opposite. –4 and 4 are opposites –4 4 • • –5–4–3–2–1 0 1 2 3 4 5 Negative integers Positive integers 0 is neither positive nor negative 2-1 Integers Integers are the set of numbers that includes all the whole numbers and their opposites, therefore, NEGATIVE numbers are included in this set. 2-1 Integers Where have you seen negative integers used? 2-1 Integers Example A Graph the integer 3 and its opposite on a number line. 3 units 3 units –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 The opposite of 3 is -3. 2-1 Integers Example B Graph the integer -5 and its opposite on a number line. 5 units 5 units –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 The opposite of –5 is 5. 2-1 Integers You can compare and order integers by graphing them on a number line. (using >, <, =) 2-1 Integers On a number line, the value of the numbers increase as you move to the right and decrease as you move to the left. Therefore, if you plot two numbers on a number line, the one that is further to the right will be the number with the greater value. 2-1 Integers Example C Use a number line to compare 4 and -4. –7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 4 is farther to the right, therefore -4 < 4. 2-1 Integers Example D Use a number line to compare -5 and -1. –7–6–5–4–3–2 –1 0 1 2 3 4 5 6 7 -1 is farther to the right , therefore -1 > -5. 2-1 Integers Example F Use a number line to order the integers from least to greatest. –3, 5, –4, 2, 0, –1 –8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 The numbers in order from least to greatest are –4, –3, –1, 0, 2, and 5. 2-1 Integers A number’s absolute value is its distance from 0 on a number line. Distance can never be negative!! So absolute value is always positive or zero. 2-1 Integers Absolute value is sometimes abbreviated ABS. The symbol for absolute value is a . 2-1 Integers Example G Use a number line to find each absolute value. |2| 2 units –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 2 is 2 units from 0, so |2| = 2. 2-1 Integers Example H Use a number line to find each absolute value. |-3| 3 units –8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 -3 is 3 units from 0, so |-3| = 3. 2-1 Integers Example I For each value of x find |x|. X=5 X = -9 X=0 2-1 Integers Lesson Quiz: Part I Compare. Use <, >, or =. 1. –32 32 < 2. 26 |–26| = 3. –8 –12 > 4. Use a number line to order the integers –2, 3, –4, 5, and –1 from least to greatest. • • • –5–4 –3 –2–1 0 • • 1 2 34 5 –4, –2, –1, 3, 5 2-1 Integers Lesson Quiz: Part II Use a number line to find the absolute value. 5. -3 3 units • –5 –4 –3 –2 –1 0 1 2 3 4 5 3 2-1 Integers Lesson Quiz for Student Response Systems 1. Identify the symbol that compares the given integers. –24 A. < B. > C. = D. ≥ 24 2-1 Integers 2. Identify the symbol that compares the given integers. 32 A. < B. > C. = D. ≤ |–32| 2-1 Integers 3. Identify the symbol that compares the given integers. –9 A. < B. > C. = D. ≤ –18 2-1 Integers 4. Use a number line to order the integers from least to greatest. –4, 5, –7, 8, –2 A. –2, –4, –7, 5, 8 B. –7, –4, –2, 5, 8 2-1 Integers 5. Identify the number line that shows the absolute value |–4|. A. 8 B. 4