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Learning Goals 7th Grade Extended Class Chapter 2: Properties of Real Numbers 1. To graph real number using a number line. 2. To compare real numbers. 3. To find the opposites and absolute values of real numbers. 4. To add integers with the same sign and different signs. 5. To subtract integers. 6. To add real numbers. 7. To subtract real numbers. 8. To organize data in a matrix. 9. To add and subtract matrices. 10. To multiply and divide integers. 11. To multiply real numbers. 12. To divide real numbers. 13. To use real numbers to model real-life problems. 14. To use all four operations of real numbers to solve a real-life problems. 15. To use the distributive property. 16. To simplify expressions by combining like terms. 7th Grade Extended Class Name: _________________________________ Chapter 2 Binder Sheet Class Color: _____________________________ Day 1 Lessons and Homework Lesson 2.1 The Real Number Line Homework: The Real Number Line Wksht 2 Lesson Adding and Subtracting Integers Homework: Adding and Subtracting Integers Wksht 3 Lesson 2.2 Addition of Real Numbers Homework: Addition of Real Numbers Wksht 4 Lesson 2.3 Subtraction of Real Numbers Homework: Subtraction of Real Numbers Wksht 5 Quiz Lesson 2.1-2.3 6 Lesson 2.4 Adding and Subtracting Matrices Homework: Matrices Wksht (Both Sides) 7 Lesson Multiplying and Dividing Integers Homework: Multiplying and Dividing Integers Wksht 8 Lesson 2.5 Multiplication of Real Numbers Homework: Multiplication of Real Numbers Wksht 9 Lesson 2.7 Division of Real Numbers Homework: Division of Real Numbers Wksht 10 Review of Multiplying and Dividing Real Numbers Homework: More Practice of Multiplication and Division of Real Numbers Wksht 11 Quiz Lesson 2.4, 2.5, 2.7 12 Lesson 2.6 Combining Like Terms Homework: Combining Like Terms Wksht 13 Lesson 2.6 The Distributive Property Homework: The Distributive Property Wksht Due Date 14 Lesson 2.6 Combining Like Terms and the Distributive Property Homework: Combining Like Terms and the Distributive Property Wksht 15 Quiz Lesson 2.6 16 Review Chapter 2 Homework: Chapter 2 Practice Test 17 Review Chapter 2 Homework: Study for Test 18 Chapter 2 Test Homework: Review Question A 19 Review Question B The binder sheet is subject to change. * Worksheets have been adapted from Algebra 1 (2004) McDougall Littell Inc Name _________________________________________________________ The Real Number Line Tell whether each number is an integer. Write Yes or No. 1. -3 2. 4.1 3. -1/2 4. 2 5. 0 6. -3.14 Use positive and negative signs to write each number. 7. Earned $50 8. 5 ft below sea level 9. Lost 10 yards Write the opposite of each number. 10. 3 11. -56.2 12. 250 13. 2.8 14. -245 16. 1 4 3 Find the absolute value of each number. 17. |23| 18. |-2.3| 20. |-1089| 21. |9| 19. |6.61| 1 1 22. |-4 2| Complete the statement using < or >. 23. 4 _____ -2 24. 2.4 _____ -2.5 25. -3.2 _____ -3.02 26. 5.1 _____ 5.01 27. 2.8 _____ 2.79 28. -4 _____ -44 Tell whether the equation or inequality is true for some values of x, all values of x, or no values of x. If it is true for some values, describe when it is true and when it is false. 29. │x│≥ 0 30. │x│= x Name _________________________________________________________ Adding and Subtracting Integers Worksheet Add or subtract the integers. Don’t forget to use the rules. ifferent ame ign um Signs ifference Subtraction Stay, change, change Follow Addition Rules 1. -23 + 57 = 2. -18 + (-13) = 3. 34 + 82= 4. -17 + 8 = 5. -67 + (-17) = 6. -71 + (-22) = 7. -78 + 16 = 8. -14 + 9 = 9. 16 + 37 = 10. 28 + (-10) = 11. -65 + (-18) = 12. -71 + 35 = 13. 84 + (-23) = 14. 47 + (-75) = 15. 62 + 14 = 16. -55 + (-55) = 17. 123 + (-60) = 18. -42 + 42= 19. -3 – 33 = 20. -43 – 71 = 21. -2 – (-56) = 22. 75 – (-83) = 23. -61 – 26 = 24. 36 – 72 = 25. -63 – (-79) = 26. -87 – (-31) = 27. 20 – (-41) = 28. -25 – 88 = 29. -36 – 78 = 30. 12 – 96 = Name _________________________________________________________ Addition of Real Numbers Worksheet Add the real numbers to find each sum. 1. 7 + 4 2. -5 + (-3) 3. 6 + (-2) + (-7) 4. -44 + 92 + (-84) 5. 19 + (-19) 6. 47 + (-95) + 12 7. -4.2 + 7.34 + 3 8. 7.15 + (-6.1) 9. 5.795 + (-5.871) 10. -16.17 + 38.143 11. 23.14 + (-12.78) 12. -15.4 + (-25.97) 1 13. − 5 + 16. 1 + 3 4 4 2 5 14. 3 + (− 8) 5 1 + (− 4) 5 17. 1 2 + (− 3) 11 4 7 15. −7 7 + (−3 8) 18. 1 2 3 + (− 3) + (− 7) 2 19. You are picking up your friend and going to a concert. Your friend lives 3 miles west of your house and the concert is 21 miles east of your friend’s house. When you are at the concert, how far away from home are you? 20. The New England Patriots’ quarterback was sacked and lost 20 yards on first down. On second down, a 25 yard pass was completed. On third down, the Patriots rushed for 6 yards. Did the Pats get a first down (a gain of ten yards)? How many net yards did they gain? Name _________________________________________________________ Subtraction of Real Numbers Worksheet Subtract the real numbers to find the difference. 1. -33 – 12 2. 45 – (-12) 3. -39 – (-45) 4. -2 – 7 5. 8 – (-3) - 2 6. 5 – (-5) - 7 7. 88.2 – (-30.4) 8. -18.14 – 3.7 9. 22.47 – (-17.38) 10. -75.4 – (-75.9) 11. -147.2 – (-56.8) 12. -136.7 – 67.3 + 4.5 13. 7 8 1 2 14. − 3 − − (− 2) 4 4 1 15. −7 9 − 2 3 5 16. The highest temperature ever recorded in Hawaii is 100°F. The lowest temperature ever recorded is 14°F. What is the range in temperatures? 17. Connor is a scuba diver at a depth of 52.8 feet below sea level. Thirty minutes later, he is at a depth of 40 feet below sea level. What is his change in depth? Did he go up or down? 18. The table shows the high temperatures for a week in May. Determine the change in temperature each day. Find the total of these changes to discover the net change in temperature. Day Temp.(°F) Sun 76° Mon 72° Tues 80° Wed 75° Thurs 75° Fri 74° Sat 78° Name ____________________________________________________ Matrices Worksheet Determine the resulting matrix through addition. 3 7 1 2 1) 1 4 5 3 4 9 6 2 3 4 2) 2 2 3 1 2 1 2 5 2 4 7 9 3) 3 6 2 3 2 1 9 0 6 7 5 4 2 1 4) 3 2 1 3 1 6 7 0 Determine the resulting matrix through subtraction. 4 2 3 1 5) 5 1 5 7 1 6 4 2 6) 3 5 7 2 0 9 4 7 5 8 1 2 4 3 1 3 7) 1 2 7 9 2 5 4 1 9 0 6 7 5 4 2 1 8) 3 2 1 3 1 6 7 0 4 2 9. Calculate the following, given R = 8 1 and S = 0 3 a) R + S b) R – S 5 1 3 5 4 3 c) S – R 2 3 1 5 10. Calculate the following, given A = and B = 4 0 7 2 a) A + B b) A – B 0 9 4 7 5 8 1 2 c) B – A 4 6 5 1 3 2 1 4 Name _________________________________________________________ Multiplying and Dividing Integers Worksheet Multiply to find the product. 1. 8 * 9 2. -8 * (-9) 3. 27 * (-5) 4. -14 • 10 5. -45 • (-12) 6. 100 • (-10) 7. (-16)(7) 8. (-25)(5) 9. -2(2) 10. (-1)(-2)(-3) 11. 5 • (-4) • (-6) 12. 10 * (-7) * (-8) Divide to find the quotient. 13. -18/(-9) 14. -40/(-5) 1 5. -256/(-16) 16. -1000 ÷ 125 17. -105 ÷ 5 18. -81 ÷ (-9) 19. -51/17 20. 63 ÷ (-7) 21. -80/5 22. -36/3/2 23. -36 ÷ (-9) ÷ (-1) 24. -56 ÷ 7 ÷ (-2) Name__________________________________________________________ Multiplication of Real Numbers Worksheet Find the product. 1. -4 * -12 2. 7(-2)(-3) 3. (-4)(-3)(-9)(3) 4. -6 * 8 * 2 * -1 5. -4.02 * 3.1 6. (-7.6)(-2.1)(-2) 2 7. − 3 ∗ 4 5 1 7 8. −3 5 ∗ (−2 8) 3 6 9. − 4 (−1)(− 7)(−2) Simplify the variable expressions. 10. 5 (-x) 11. (-4)(-x)(-x) 12. 6(-r)(-r)(-r) 13. (-3)(z2)(z) 15. (-y)2(y)2 1 16. (2)(−2𝑥) 14. -7(-d)3 5 7 17. − 7 (− 5 𝑥) 3 18. (− 4)(−𝑘)(−4𝑘) Evaluate the expression. 19. -4x when x = 3 20. -5(t)(-t) when t = -4 21. x3+2 when x = -2 22. 2y3 – 3 when y = -3 23. –x2- 5x + 7 when x = -2 24. -2(│y -5│) when y = 3 25. 2x2 - 3x + 1 when x = 2 26. 4m + m2 when m = -5 Name _________________________________________________________ Division of Real Numbers Worksheet Find the quotient. 1. -8 / 4 2. 18 ÷ (-3) 4. -18 ÷ 36 5. −80 ÷ (− 5) 7. 3. -48 ÷ (-4) 4 −24 8. 6 − 7 1 6. −13 ÷ 2 36 2 9. −33 ÷ 3 3 9 − 10 Simplify the variable expressions. 10. -15x/3 11. -6y ÷ (-3) 13. 𝑐 8 14. ÷4 6 16. −12𝑦 ÷ − 11 Evaluate the expression. 𝑥+2 19. 𝑦 when x = 8 and y = 2 21. 4𝑥−3 𝑦 when x = 3 and y = -3 3𝑏 4 12. 48x ÷ (-6) 3 5 15. −20𝑘 ÷ 6 ÷4 12 𝑥 17. 60𝑎 ÷ (− 7 ) 7 18. − 4 ÷ 16 20. 𝑥−𝑦 22. 5𝑥+2 4 𝑦 when x = 17 and y = 1 when x = -2 and y = -4 Name__________________________________________________________ More Practice Multiplying and Dividing Real Numbers Simplify the variable expression. 1. (14)(−𝑥) 2. (−2)(−𝑦)(−𝑦) 3. (−3)3 (−𝑡)2 4. −(−𝑦)2 (𝑦)2 3 5. (− 4)(−𝑘)(−16𝑘) 2 7. −16𝑥 2 ÷ (− 3) 9. − 3𝑏 8 1 ÷ (−4 2) 6. (−13)(−6𝑦) 36𝑎 9𝑎 8. − 40𝑏 ÷ −10 3 10. −15 ÷ − 5 𝑦 Evaluate the expression for the given values of the variable(s). 11. 4+𝑥 2 𝑦 , 𝑤ℎ𝑒𝑛 𝑥 = −4 𝑎𝑛𝑑 𝑦 = 2 13. 2𝑦 2 − 3 𝑤ℎ𝑒𝑛 𝑥 = −3 12. 4𝑥 2 −3 −𝑦 , 𝑤ℎ𝑒𝑛 𝑥 = 3 𝑎𝑛𝑑 𝑦 = −3 14. −𝑥 3 + 𝑥 2 𝑤ℎ𝑒𝑛 𝑥 = −2 Name _________________________________________________________ Combining Like Terms Worksheet Simplify by combining the like terms. 1) 6k + 7k 2) 12r − 8 − 12 3) n - 10 + 9n − 3 4) -4x + 10x 5) r + 10r 6) 2x + 11 - 6x 7) 11r − 7r 8) v + 8 + 12v 9) 8x + 3 + 11x + 4 10) n + 14 - 9 + 5n 11) -12r + 5 + 3r − 5 12) 5n + 18 + 12n 13) 9y + 60y + 10 14) 4x3 + 2x2 + 8x3 + 1 15) 4c + 7c2 – 2c 16) 10xy + 8x + 3y – 5xy 17) 12abc – 4abc + 2 18) 2x3 – 4 + 5x3 + 7 Name _________________________________________________________ The Distributive Property Simplify. 1. 8(3m + 4) 2. 7(2x2 – 6y) 3. ½ (8r – 12) 4. (16 + 13p)10 5. (54g + 10g2)5 6. 2 (12x + 16) 7. 4(13v – 9) 8. 3(1 + k) Factor. 9. 8x + 8 10. 20n – 15 11. 12a + 16 12. 24g – 9 13. 20 – 5r 14. 26p - 18 Name _________________________________________________________ Combining Like Terms and Distributive Property Worksheet Combine the like terms to simplify. 1. 5x + 16y - 2x – 20y 2. 16m + 7 + (– 4m) 3. 9.2x + 7.1x – 12 4. -2r + 4r2 + 7r – 18r2 5. 7 8 𝑥+ 5 9 2 𝑥+3 4 6. − 5 𝑝 − 1 2 + 1 3 𝑝+ 3 4 Use the distributive property to simplify. 7. 8(x + 5) 8. 4(y – 7) 9. -6(r -1) 10. -12(3 + m) 11. y2(2 – 3y) 12. -3x(-x - 5) 13. –a(a + 2) 14. –(4t – 8) Use the distributive property and combine like terms to simplify. 15. 2(x + 1) + x 16. 2(3a – 5) + 2a 17. -4(5m + 2) + 3m 18. 2t + (3+ 5t)4 19. 2x(x + 4) + 5x2 20. -2m(m – 5) + (-5m2) 21. 5 + 2(a + 8) 22. 4 - 3(y + 8) 23. 7c - 2c(c + 3) 24. 9p – 8(p – 6) Name _________________________________________________________ Chapter 2 Practice Test Find the value of the expression. 1. |-7.2|- 16.4 2. -1.8 + |-7.4 - 3.1| 3. 16.23 - (-14.2) + (-9.3) 1 3 4. 7 4 3 7 Write the numbers in increasing order. 5 2 1 5. 4 , 1.5, 2.35, 2 , 2 9 5 9 Find the value. 6. A company has a loss of $213.15 in January, a loss of $57.11 in February, and a profit of $121.55 in March. What was the company’s net profit or loss over the three month period? Evaluate the expression for the given value of the variable. 7. 7 + x + (-11) + (-3) when x = 2 8. -3x3 – 5 when x = -2 9. 2|4x - 6| when x = -4 10. 6x2 + 1 when x = 1 3 Add or subtract the matrices. 8 .7 11. 2.8 3.4 3 1 4 1 4 12. 4 3 5 5 .6 6.4 12.9 + 10.5 14.12 5.1 6 2 2 3 7 6 - 1.9 3.76 7.1 2 3 1 3 2 1 4 3 10 1 1 3 2 1 5 4 Find the product or quotient. 13. (-5)(-4)(2)(-3) 15. 8y(-y)(-y)(-y) 17. (-5)3(-h)5 14. -12 ÷ 16. 42 7 8 2 3 Simplify the expression. 18. 21x2 + 27x + 36x2 + 9 19. -7.6p + 14.5p 20. (-8c2)(2c2-3c) 21. -9(2q + 3) 22. 4k + 6(3 – 7k) 23. 4y + 5(2 + y) 24. 12r – (3r + 9) 25. 4m – 5(2f - 8)