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Chapter 4.1 Compare and Order Integers

Chapter 4.1 Compare and Order Integers. Objectives: Students will be able to graph, order integers, find the opposite of a number, and find the absolute value of a number. CA Standard: Alg. 2.0. Vocabulary and Concepts. The numbers……, -4, -3, -2, -1, 0, 1, 2, 3, 4, ….are called integers.

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Chapter 4.1 Compare and Order Integers

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  1. Chapter 4.1 Compare and Order Integers Objectives: Students will be able to graph, order integers, find the opposite of a number, and find the absolute value of a number. CA Standard: Alg. 2.0

  2. Vocabulary and Concepts • The numbers……, -4, -3, -2, -1, 0, 1, 2, 3, 4, ….are called integers. • Negative integers are less than 0. They lie to the left of 0 on the number line. • Positive integers are greater than 0. They lie to the right of 0 on the number line.

  3. 4. Two numbers that are the same distance from 0 on a number line but are on opposite sides of the 0 are called opposites. For example 3 and -3. 5. The absolute value of a number a, written as /a/, is the distance between a and 0 on a number line.

  4. Example 1: Graphing and Ordering Integers Graph each integer on a number line.

  5. You Try! Order the integers from least to greatest. • -8, 5, -2, 0, 6 b. -12, 15, 3, 9, -6

  6. Example 2: Finding the Opposite of a Number. • If a = 6, then –a = ______________ b. If a = -5, then –a = ______________

  7. Example 3: Finding the Absolute Value of a Number • If a = 3, then /a/ = /3/ = __________ • If a = -8, then /-a/ = /-8/ = ___________/

  8. You Try! Write the opposite and the absolute value of the number. • 14 = b. 8= c. -10 = d. -2 =

  9. Class work Do page 164 #2=34 evens Do page 165 #2- 28 evens

  10. 4.1 Quiz Use a number line to order the integers from least to greatest. • 7, -4, 3, 0, -21, -36, 14 Write the opposite and absolute value of the integers. • -4 = c. 34 = Simplify. d. /-8/ = e. –[-(-3)] =

  11. 4.2 Add Integers4.3 Subtract Integers Objective: Students will be able to add and subtract integers. CA Standard: Gr. 7 NS 1.2 Add, subtract, multiply, and divide rational numbers.

  12. Example 1: Adding Integers Using a Number Line. a. 9+(-11)

  13. -6 +14 = • -3 + (-4) =

  14. You Try! • 2+(-5) = • -7+(-6) = • -8+5 =

  15. Example 2: Adding Integers Without a Number Line • 26-32 = • -9 -16 = • 36-(-36) = • -12-(-52) =

  16. Example 3: Adding More Than Two Integers The diagram below shows the results of four plays in a football game. On the first play, the team gained 6 yards. On the second play, the team lost 11 yards. On the third and fourth plays, the team gained 4 yards and then 9 yards. What was the total number of yards the team gained?

  17. Example 4: Subtract Integers Find the difference. • -25(- 9-8) = b. -18 -35 =

  18. Example 5: Evaluating Algebraic Expressions Evaluate a-(-b)-16 when a = 21 and b =4

  19. You Try! Evaluate the expression when x = 11 and y = -7 • 9-x b. y-x = c. 16-x-y

  20. Example 6: Using Integer Subtraction • Last year the enrollment at Oakwood School was 568 students. This year the enrollment is 492 students. Find the change in enrollment. Change in enrollment = Enrollment this year – enrollment last year

  21. Class work • Do page 170 #2-22 evens • Do page 176 # 4-32 evens

  22. Name:Date:Page Number: Use a number line to find the sum. 2. -2 +4 =

  23. 4.2 and 4.3 Quiz Find the sum. • 1. (-5) + (-6) = • 2. (-3) + (-6) = • 3. (-2) + (-8) = • 4. (-9) + (+10) = • 5. (-29) + (-11) = Find the difference. • 6. 5 – (- 8) = • 7. –7 – (+8) = • 8. –9 – (+ 4) = • 9. 9 – (-2) = • 10. –1 – 6 =

  24. 4.4 Multiply Integers4.5 Divide Integers Objective: Students will be able to multiply and divide integers. CA Standards:Gr. 7 NS 1.2 Add, subtract, multiply, and divide rational numbers.

  25. Multiply and Divide Integers - (-) - ÷ - = + - (+) - ÷ + = - + (+) + ÷ + = + **** Odd numbers of negatives (1, 3, 5,etc.) = - (negative) Even numbers of negatives (2, 4, 6, etc..) = + (positive)

  26. Example 1: Multiplying Integers • -6(-9) = • -7(3)(-2) = • -5(0) = • -9(-4)(-3) =

  27. Example 2: Compare Integer Product. • 3(-4)_____ (-3)(-4) • 5 ● |7|_____ |6|● (-8)

  28. Example 3: Evaluating Variable Expressions with Integers Evaluate 2a - b2 when a = -12 and b = -4

  29. Example 4: Dividing Integers • -36 / -12 = • -56 / 8 = • O / -18 =

  30. Example 5: Finding the Mean • The mean is the average. a. 21, -53, -46, 32, -14

  31. Find the mean of the data. The table shows the average monthly high Temperature for the coldest months In Barrow, Alaska. What is the mean high temperature for these months?

  32. You Try! 1. -5(6) = 2. -3(2)(-4) = 3. -12(-1) = 4. 7(-2)(4) = 5. -58/-1 = 6. 38/-2 =

  33. Find the mean 7. 25, -26, -25, 46, -55 = 8. -3, 0, 4, 5, -2, 8 =

  34. Class work • Do page 184 #1-36 every 4 numbers • Do page 190 # 1-36 every 4 numbers ( 4, 8, 12, etc…)

  35. 4.4 and 4.5 Quiz • (-7)(-3) = • 11(-6) = • -9 ÷ 3 = Evaluate the expression when a = -24, b = -6, and c= -12 4. ac ÷ b 5. Find the mean of the numbers. -16, 2, -18, 4, -11, -8, -6, 5

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