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PRE-ALGEBRA Summer Packet VANDEBILT CATHOLIC HIGH SCHOOL Incoming 8th Grade EXAMPLES Section I Objective: Write an algebraic expression to represent unknown quantities with one unknown and 1 or 2 operations Examples: The examples below show algebraic expressions written as mathematical 9 more than a number the sum of 9 and a number x+9 a number plus 9 a number increased by 9 the total of 4 subtracted x and 9 from a number a number minus 4 h-4 4 less than a number a number decreased by 4 the difference of hand 4 6 multiplied by 9 6g 6 times a number the product of 9 and 6 a number divided by 5 the quotient of t and divide a number by 5 5 t 5 expressions. Section II Objective: Simplify using given operations and by combining like terms Examples: The examples below show how to simply expressions by combining like terms and performing indicated operations. 2x + 4x-7 Determine 6x-7 Combine like terms 2(x + 3) - 5x Distribute 2x + 6 - 5x Determine -3x+ like terms 6 like terms Combine like terms Section III Objective: Solving equations for missing variables Examples: The examples below show how to solve equations using addition, subtraction, multiplication, and division. 2x +5 = 7 Use inverse operations -5 -5 Subtract 5 from both sides 2x +2 =2 Isolate x +2 Divide 2 on both sides x=l to isolate the variable = 3 (2x - 1) 6x - 3 21 = 21 +3 +3 6x = 24 Distribute Use inverse operations to isolate 6x Add 3 to both sides Isolate x Divide 6 on both sides x=4 Section IV Objective: Solving proportions Examples: The examples below show how to solve proportions x 24 12 3 12 x 24 288 Cross multiply to solve for the missing value =3xx = 3x -;- 3 -;- 3 2 = Multiplication Isolate x Divide 3 on both sides = 96 x X by cross multiplication. 14 Cross multiply to solve for the missing value 7 2 x 14 28 = 7xx = 7x -;-7 -;-7 x=4 Multiplication Isolate x Divide 7 on both sides Section V Objective: Performing operations with negative integers Examples: The examples below show how to perform operations with negative integers. These are just some of the possibilities. -4x 6 = = Negative Negative -;-Positive = Negative -4 -3+5 = Negative + Negative -8 -24-;-.6 = = Negative -24 -3+ -5 = Negative x Positive Negative + Positive 2 = Takes the sign of the integer with the larger absolute value Examples: Rational Numbers: Helpful processes and tips Multiplying Fractions and Mixed Numbers 1. Change any mixed numbers to improper fractions 2. Cross cancel any numerator with any denominator by dividing each by a common factor 3. Multiply numerators together 4. Simplify ...put fraction in simplest form (keep as an improper fraction) then multiply denominators together Dividing Fractions and Mixed numbers 1. Change any mixed number to an improper fraction 2. Keep the first fraction, change the division sign to a multiplication fraction sign and flip the second this means multiplying by the reciprocal 3. Multiply numerators together 4. Simplify ...put fraction in simplest form (keep as an improper fraction) then multiply denominators together Adding and Subtracting Fractions and Mixed Numbers 1. Change any mixed number to an improper fraction 2. Find common denominators 3. Keep the denominator and add numerators 4. Simplify ...put fraction in simplest form (keep as an improper fraction) Section VI Objective: Solving expressions using order of operations Examples: The examples below show how to solve expressions using order of operations. First, let's recall Order of Operations. Parenthesis Exponents Multiplication Division Addition & (left to right) & 5 ubtraction (3 + 1) + 4 + 24 4+6 = 10 (left to right) (4 -i- x 6) -;-4 4 Do what's inside of the parenthesis Division Add Section VII Objective: Graph given coordinates Examples: The examples below show how graph ordered pairs onto a coordinate plane. First, let's recall Quadrants. --1- I Y I Quadrant II (-, +) - Quadrant! (+,+) 2 Graphing Ordered Pairs: -s s 0 x Quadrant Ilf -2 2. Move along the y-axis second 3. Plot the point and label with the given variable Quadrant IV (+, -) (-, -) 1. We move along the x-axis first -s r.. .• Graph the following ordered pairs: E .. '. :;. ~ A (1,3) /J. B B (3,1) • ~ C (3,-3) ., - D (-4,2) '} c • ,.,f' E (-1,5) .; c -, F (-3,-3) Section VIII Objective: Order rational numbers on a number line Examples: The examples below show how use a number line to help order rational numbers from least to greatest. First, let's recall negative and positive integers and the number line . •• I I I I I I I I I I I , I I I I I I I I I ~ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 negative 0 1 2 3 4 zero 5 6 7 8 9 10 positive 14 20} Order the rational numbers from least to greatest: 1. 6 3 5 } 10 Change fractions to decimals 2. Use the number line to plot the points 3. Rewrite using the original rational numbers -1.2 -0.4 < I : I + I II I I I I t I I -1 I /I o 0.3 t I I I 0.7 + I II I I I I) 1 Section IX Objective: Find area and perimeter of shapes Examples: These are the formulas that must be used to find the area and perimeter of the geometric figures. Area 0'a polygon = The amount of space inside the boundary of a flat (2- dimensional) object Perimeter 0'a polygon the sum of the sides Formulas + 2w A = lw 51 + 52 + 53 + 54 A = bh = 51 + 52 + 53 A = = 51 + 52 + 53 + 54 Rectangle: P = 21 Square: P = 45 Parallelogram: P = Triangle: P Trapezoid: P Circle: Circumference = ttd !bh 2 VANDEBILT CATHOLIC mGH SCHOOL PRE-ALGEBRA © 2016 Kuta Software LLC. All rights reserve d. Incoming 8th grade Summer Packet Please show your work for all problems given. Make sure you BOX off your answers. Please refer to the example problems attached to the packet if you have any questions or need any guidance. I. Write each as an algebraic expression when given as a verbal expression and as a verbal expression when given an algebraic expression. 1) 29 decreased by 4 2) the product of 9 and x 3) 3 increased by 8 4) the sum of2 and n 5) 12Y 6) c - 16 7) 4 + v 8) n + 5 t'J 2016 KutaSoftware LLC. All rights reserved.-1JlVfadc with Infinite Algebra 1. Il. Simplify each expression by combining like terms where necessary. 9) 4 + 3r + 8 10) 2 + 5x - 3x + 7 ll)n+l-n 12) 1 - lOp - 4p 13) 4x+ 3x 14) 6a - 8 + lOa © 2016 Kuta SoftwarcLLC. All rights rescTved"72-Made with Tnfinite Algebra 1. III. Solve each equation given. 15) v- 5 =-4 17) 4=- 16) 2 = a-7 x a 18) -= -16 19 20 19) 36 = 17 + x 21) -3 =a- 20) 13=-4+b 19 x 22) 3 =12 23) 15 = -5n © 2016 Kuta 24) -2=x+ Software LLC. All rig h t s res e r v e d -:-3- Mad c wit 13 h J n fi nit e A I g e bra I . 25) 5n = 70 26) 20 = 2x + 8x 27) -1 = 3 - 8k + 4 28) -7k- 4 + 6k= -12 29) -5 = 7 + 6x + 6x 30) -4=-3a+4a 31) -5(7m - 5) = -115 32) 6(1 - 4a) = 126 33) -7(3x - 6) = -84 34) 5(3b - (:) 2 0 16K u [a S 0 f t w aTe L L C. All rig h t S T e s e r v e d -4- Mad e wit 5) = -100 h T n fin i teA 1 g c bra I. IV. Solve each proportion. 9 2 35) x 4 4 9 36) -=m 6 5 m 37) -=10 9 9 x 39) -=8 3 «) 2 0 16K v 2 -=- 40) !=~ 6 n uta S 0 f 1 war eLL C. All rig h t s res c r v e d . 5 38) -5M a dew 3 i t h I n fin i teA 1 g e bra I V. Operation practice with negatives 42) -35 41) 90 9 43) -7 Q 44) 90 -4 -9 46) (-6)(4) 45) (-9)(-10) 47) © (-2)(-1) 2 0 16K uta 48) Soft war eLL C . All rights reservetr.6- Made (-7)(-2) with Infinite Algebra I. 3 5 49)1--4 3 1 4 50) - -5 3 3 51) 1- 28 2 52) -1-15 2 53)-1-- 3 e 2016 Kuta 9 -- 5 Software 3 5 2 6 54) - +-2- LLC. All rightsreservcd:-7-MadewithTnfinitc Algebra I. VI. Order of operations. Use order of operations to simplify each expression. 55) 4 + 4 + 6 x 3 - 4 56) 5 - (1 + 1 + 3) 7 5 58) 3 - 3 + 4 x 3 x 3 o 20 J 6 K uta S 0 f t 2) x 60) (5 - 59) 187(3+6-6)+1 war eLL C. A 11 rig h ts res e r v ESt. Mad e wit 87 (6 - h I n fin 2) i teA I g c bra 1. VII. Graph each ordered pair. Label with the corresponding letter. 61) G (1,0), R (-3, 1), V (-2, -3) , I j 62) A (3,2), B (-4, 1), C (-5, -2) y y ! I ,Is I I i2 k '6 14 8 x 63) F (-1-5), M (3,5), P (-4,3) 2 " I 6 x 64) T (0,0), P (4, -2), S (-5, -4) y y I I I I 14 6 ? J6 8 X , - x I I © 20 16K uta S 0 f t war eLL C. A I I rig ht s res e r v e d . -G- a dew i t h Tn fin i teA I g e bra I . VID. Order from least to greatest. Look at each rational number. Put them on a number line. Order them from least to greatest using their original forms. 2 5 65) 1.4, -, 3 67) 23 It') 2 0 16K 2 7! 3' 8.4, 54 68) - 0 f t war eLL 714 io ' 9 S 1 2-, 2 '2 3 2' uta 66) ,.71 C. All T i g h t 5 res e r v e-J 0- Mad e 2' wit 2.4, 2.1 0.4, h T n fin 5 i teA I g e bra 1. IX. Find the area and perimeter of each. 69) A square with a side length of 4 inches. 70) A triangle with a height of 4 inches and sides of 5 inches, 9 inches and 7.5 inches. 71) A rectangle with a width of 12 centimeters and a length of21 centimeters. 72) A parallelogram with a side lengths of 20 centimeters top and bottom and 10 em on each side with a height of 8 em. 73) A rectangle with a length of 3 yards and a width of 1.5 yards. e 2016 Kuta Software LLC. All rights rcservell1.1- Made with Infinite A Igebra I.