Summer Packet 7 th into 8 th grade 1 Integer Operations Name Adding Integers If the signs are the same, add the numbers and keep the sign. 7 + 9 = 16-2 + -6 = -8 If the signs are different, find the difference between the numbers and keep the sign of the number with the greater absolute value. 5 + -11 = -6-10 + 12 = 2 Subtracting Integers Change the subtraction to addition and the next number to its opposite. Then follow the rule for addition. (a.k.a. Add a line, change the sign.) 6 4 6 + -4 = 2-10 - -8-10 + 8 = -2 Multiplying and Dividing Integers Multiply or divide. If there are an odd number of negatives, your answer will be negative. If there is an even number of negative signs, your answer will be positive. -5-3 = 15 (-1)(5)(2) = -10 16-56 -8 = 7 = 4 4 1. 33 + -48 = 2. 240-6 = 3. -5 + -13 = 4. -288-24 = 5. -6-5 -4 = 6. 15 - -28 63 14 = 144 7. = 8. -53 + 20 + -7 + -14 + 13 = 12 9. -137 45 = 10. 0-12 =
Summer Packet 7 th into 8 th grade 2 Absolute Value Absolute Value the distance a number is from zero on the number line. Ask yourself: How far is the number from zero? 31 = 31-16 = 16-12 + 8 = -4 = 4 11. -1234 = 12. 97 = 13. 20 + -25 = 14. -7 + 13 = Order of Operations Solve the following problems. Show your work. Be sure to follow the order of operations. Parenthesis Exponents Multiplication or Division: Whichever comes first from left to right. Addition or Subtraction: Whichever comes first from left to right. Example: 8 4 2 + 2 = 8 2 + 2 = 6 + 2 = 8 15. 12 3 + 12 4 = 16. (21 7 + 4) 11 = 17. 144 16 9 3 = 18. -15 8 + -4 - -6 = 19. (-72 9)(-15-5) = 20. -6[7 (-225 15) 3] = 21. (5 + -18 2)(16 4 2 36 2 ) = 22. = 67 70 2
Summer Packet 7 th into 8 th grade 3 Fraction Computation Adding and Subtracting Fractions Change all mixed and whole numbers to improper fractions if necessary. Find a common denominator. Add/subtract the numerators. Simplify your answer. Example: 1 1 1 2 3 1 + = + = = 6 3 6 6 6 2 1 7 4 7 12 7 1 = 1 = = 2 8 8 8 8 8 5 8 Multiplying and Dividing Fractions Remember, when multiplying and dividing fractions there is no need to have a common denominator. Change all whole and mixed numbers to improper fractions. If it is a division problem, don t forget to change it to multiplication, and flip the 2 nd fraction. Cross cancel then multiply. Example: 2 1 11 9 11 2 3 4 = = = 3 2 3 2 3 9 22 27 23. 7 5 1 5 = 24. 3 + = 8 6 6 12 25. 6 5 4 = 26. 5 2 = 5 6 5 27. 1 3 2 = 28. 2 4 1 7 = 2
Summer Packet 7 th into 8 th grade 4 Ordering Fractions and Decimals Write the following numbers in order from least to greatest. It might be helpful to write all fractions with a common denominator or to use a number line. 29. 3, 8 3 5,, 4 6 2 3 30. -6.404, -6.04, -6.044 Decimal Computation Adding and Subtracting Line up the decimal points and fill in zeros when needed. 31. 202.554 + 39.75 = 32. 3.056 2.678 = 33. 7.9 + -3.8 = 34. 1.5 - -3.4 = Multiplying and Dividing Decimals Multiplying decimals is the same as multiplying whole numbers. The key is to count the decimal places in each factor. Step 1: Line up the digits (not the decimal points) Step 2: Multiply as with whole numbers. Step 3: Count the decimal places in the problem. The product (answer) has the same number of decimal places. Dividing decimals (by whole numbers) is the same as dividing whole numbers. Divide as usual. Then bring the decimal in the dividend straight up to the quotient. 35. -8.1 4.5 = 36. 4 18. 4
Summer Packet 7 th into 8 th grade 5 Two-Dimensional Geometry and Measurement Angles Two angles are complimentary angles when the sum of their measures is 90 Two angles are supplementary angles when the sum of their measures is 180 Two angles are vertical angles when they are opposite angles formed by the intersection of two lines. Vertical angles are congruent angles, meaning they have the same measure. Tell whether the angles are complimentary, supplementary, or vertical. Then find the value of x. 37. 38. 39. Interior Angle Sums The sum of the interior angles of any polygon is known as the interior angle sum. -The sum of the angle measures of a triangle is 180 -The sum of the angle measures of a quadrilateral is 360 Name each polygon. Then find the values of the missing angles. 40. 41. 42. 43. x y x name name name name x = x = x = x = y =
Summer Packet 7 th into 8 th grade 6 Two-Dimensional Geometry and Measurement Use the formula sheet to find the area AND perimeter of each shape. Round to the nearest hundredths when necessary. Use 3.14 for π (pi). Triangle Example: A = 2 1 b h 5m A = 2 1 8 5 8m A = 20 m 2 44. A = 46. d = A = 45. P = 8 yd 47. r = C = 20 cm 8 yd 48. P = 50. P = 49. A = 4 cm 51. A = 5ft. 4ft. 5ft. 6 cm 6ft. 6m 52. A = 54. A = 53. P = 13m 12m 13m 55. P = 5 in 16m 3 in 6 in. 1 in.
Summer Packet 7 th into 8 th grade 7 Equations Here are a couple hints for solving equations: -combine like terms -isolate the variable to one side of the equal sign (equation). -use inverse operations to undo (add/subtract & multiply/divide). Example: n 6 = 21 + 6 +6 n = 27 Solve the equation. Check your solution. 56. 8 = q + 15 57. 2y 3y = 5 58. 4 n 2 p = 59. = 7 11 5 Distributive Property Multiply the number on the outside of the parentheses by each term inside the parentheses. Don t forget the rules for negatives! Draw rectangles or arrows if you need to. m 3 4 60. 10(a 4) = 61. 7(x + y) = 62. -4(k + -9) = 63. 3(-7x 5) = 1 2 64. ( 48x 25t) =
Summer Packet 7 th into 8 th grade Example using the vertical method: 8 (s + 12) + (3s 8) Expressions Find the sum or difference. (s + 12) +(3s 8) 4s + 4 ( 4 3) ( 2) 65. y + y ( 3 7) ( 5 6) 66. p + p ( 3 7 ) 2( 3.5 1) 67. m + m + ( 5 9) 38 ( 2 ) 68. b b Inequalities -An inequality is a mathematical sentence that compares expressions. -An open circle is used when a number is not a solution. -A closed circle is used when a number is a solution. Steps for Solving and Graphing Inequalities: 1) Use operations to isolate the variable to one side of the inequality. 2) Mark and label your number line. 3) Draw either an open or closed circle (depending on the problem you are solving). 4) Draw the arrow. Example: x 2 < 3 +2 +2 x < 5 Solve the inequality. Graph the solution. -2-1 0 1 2 3 4 5 6 7 69. w 8 4 70. x 4 5 > 1 5 1 3 2 < 5 4 71. ( x )
Summer Packet 7 th into 8 th grade 9 HINT: (x,y) or (across, up/down) Coordinate Graphing Plot the following points on the graph. Be sure to label your points with the letter. 72. A (3,2) 73. C (0, -5) Find the coordinates. 74. D ( ) 75. E ( ) 76. What are the coordinates of the origin? Data Analysis Mean add up the values and divide by the number of values Median the middle value in an ordered set of values Mode the value that occurs the most Range the difference between the highest and lowest value in a set of data Use the following data set to complete the next four problems. Round to the hundredths place when necessary. 112, 117, 121, 112, 118, 118 77. Mean - 78. Median - 79. Mode - 80. Range - Probability Suppose you have a bag of 20 marbles: 2 blue, 4 red, 8 yellow, 6 green. Use this information to complete the following 2 problems. Write each answer as a fraction, decimal, and percent. 81. What is the probability of grabbing a red marble? 82. What is the probability of grabbing a purple marble? 83. What is the probability of grabbing a blue or green marble?
Summer Packet 7 th into 8 th grade 10 Proportions Find the missing value. Round to the nearest hundredth when necessary. Use scale factor or cross multiplication. 84. 3 n 2.5 10 = 85. = 6 24 4 x 86. 1 c 5 n = 87. = 2 7 9 5. 4 Percents Remember; turn your percentages into decimals before multiplying. Example A What is 20% of 100? Think 20% of 100 is? So 0.20 x 100 = _20_ Hint: It is possible to have a percent greater than 100! Example B 12 is what % of 60? Think What % is 12 of 60? Place the part (12) over the whole (60) and reduce. So 12/60 = 1/5 = 0.20 Change the fraction or decimal to a percent. 1/5 or 0.20 = 20% 88. 32 is what % of 200? 89. What number is 80% of 65? Use the original price and percent discount to find the sale price. 90. Original price: $80 91. Original price: $42 Discount: 20% Discount: 15% Sale price: Sale price: Example: Original price: $50 Discount: 10% 1 0% of $50 = $5 So, $50- $5 = $45 Sale price: $45 92. Original price: $120 93. Original price: $112 Discount: 80% Discount: 32% Sale price: Sale price:
Summer Packet 7 th into 8 th grade 11 Three-Dimensional Geometry and Measurement 94. If you are asked to cover a solid, you should find its. 95. If you are asked to fill a solid, you should find its. Directions: -Use the formula sheet to find the surface area AND volume of each cylinder. -Show all work including formulas used and values for each letter or symbol. -Round to the nearest hundredths when necessary. -Use 3.14 for π (pi). 96. 97. volume = surface area= volume = surface area= 98. The rectangular prism has: (How many of each?) faces, edges, and vertices. 99. Find the volume of the rectangular prism. 100. Find the surface area of the square pyramid. 11cm 12cm