PRE-ALGEBRA Summer Packet VANDEBLT CATHOLC HGH SCHOOL ncoming 8th Grade EXAMPLES Section Objective: Write an algebraic expression to represent unknown quantities with one unknown and 1 or 2 operations The examples below show algebraic expressions written as mathematical expressions. 9 more than a number the sum of 9 and a number a number plus 9 a number increased by 9 the total of x and 9 x+9 4 subtracted from a number a number minus 4 4 less than a number a number decreased by 4 the difference of hand 4 h-4 6 multiplied by 9 6 times a number the product of 9 and 6 6g a number divided by 5 the quotient of t and 5 divide a number by 5 t 5
Section Objective: Simplify using given operations and by combining like terms The examples below show how to simply expressions by combining indicated operations. like terms and performing 2x + 4x-7 Determine like terms 6x-7 Combine like terms 2(x + 3) - 5x Distribute 2x + 6-5x Determine like terms -3x+ 6 Combine like terms Section Objective: Solving equations for missing variables The examples below show how to solve equations using addition, subtraction, multiplication, and division. 2x + 5 = 7 Use inverse operations to isolate the variable -5-5 Subtract 5 from both sides 2x = 2 solate x +2 +2 Divide 2 on both sides x=l
3 (2x - 1) = 21 Distribute 6x - 3 = 21 Use inverse operations to isolate 6x +3 +3 Add 3 to both sides 6x = 24 solate x x=4 Divide 6 on both sides Section V Objective: Solving proportions The examples below show how to solve proportions by cross multiplication. x 24 12 3 Cross multiply to solve for the missing value 12 x 24 = 3 x x Multiplication 288 = 3x solate x -;- 3 -;- 3 Divide 3 on both sides x = 96 X 14 = 2 7 Cross multiply to solve for the missing value 2 x 14 = 7 x x Multiplication 28 = 7x solate x -;-7 -;-7 Divide 7 on both sides x=4
Section V Objective: Performing operations with negative integers The examples below show how to perform operations with negative integers. These are just some of the possibilities. -4x 6 Negative x Positive = Negative = -24-3+ -5 Negative + Negative = Negative = -8-24-;-.6 Negative -;-Positive = Negative = -4-3+5 Negative + Positive = Takes the sign of the integer with the larger = 2 absolute value 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 then multiply denominators together 4. Simplify...put fraction in simplest form (keep as an improper fraction) 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 sign and flip the second fraction this means multiplying by the reciprocal 3. Multiply numerators together then multiply denominators together 4. Simplify...put fraction in simplest form (keep as an improper fraction) 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 V Objective: Solving expressions using order of operations The examples below show how to solve expressions using order of operations. First, let's recall Order of Operations. Parenthesis Exponents Multiplication & Division (left to right) Addition & 5 ubtraction (left to right) (3 + 1) + (4 x 6) -;-4 Do what's inside of the parenthesis 4 + 24 -i- 4 Division 4+6 Add = 10
Section V Objective: Graph given coordinates The examples below show how graph ordered pairs onto a coordinate plane. First, let's recall Quadrants. --1- Y - Quadrant Quadrant! (-, +) (+,+) 2 Graphing Ordered Pairs: -s 0 s x Quadrant lf Quadrant V -2 (-, -) (+, -) 1. We move along the x-axis first 2. Move along the y-axis second 3. Plot the point and label with the given variable -s :;. ~ ~., E. r.... '. /J. B Graph the following ordered pairs: A (1,3) B (3,1) C (3,-3) D (-4,2),., f' -'} c E (-1,5).; c F (-3,-3) -,
Section V Objective: Order rational numbers on a number line The examples below show how use a number line to help order rational greatest. numbers from least to First, let's recall negative and positive integers and the number line., ~ -10-9 -8-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 8 9 10 negative zero positive Order the rational numbers from least to greatest: 14 6 3 20} 5 } 10 1. Change fractions to decimals 2. Use the number line to plot the points 3. Rewrite using the original rational numbers -1.2-0.4 < : + t -1 0.3 0.7 / t + o ) 1
Section X Objective: Find area and perimeter of shapes These are the formulas that must be used to find the area and perimeter figures. of the geometric 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 Rectangle: P = 21 + 2w A = lw Square: P = 45 Parallelogram: P = 51 + 52 + 53 + 54 A = bh Triangle: P = 51 + 52 + 53 A =!bh 2 Trapezoid: P = 51 + 52 + 53 + 54 Circle: Circumference = ttd
PRE-ALGEBRA VANDEBLT CATHOLC mgh SCHOOL 2016 Kuta Software LLC. All rights reserve d. Summer Packet ncoming 8th grade 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.. 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 nfinite Algebra 1.
l. 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.
. Solve each equation given. 15) v- 5 =-4 16) 2 = a-7 x 17) 4=- 20 a 18) -= -16 19 19) 36 = 17+ x 20) 13=-4+b 21) -3 = a - 19 x 22) 3 =- 12 23) 15= -5n 24) -2=x+ 13 2016 Kuta Software LLC. All rig h t s res e r v e d -:-3- Mad c wit h J n fi nit e A g e bra.
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 - 5) = -100 (:) 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 h T n fin i tea 1 g c bra.
V. Solve each proportion. 9 2 35) x 4 4 9 36) -=m 6 5 m 37) -=- 10 9 v 5 38) -=- 2 6 9 x 39) -=- 8 3 40)!=~ n 3 «) 2 0 16K uta S 0 f 1 war ell C. All rig h t s res c r v e d. -5M a dew i t h n fin i tea 1 g e bra
V. Operation practice with negatives 41) 90 9 42) -35-7 43) Q -4 44) 90-9 45) (-9)(-10) 46) (-6)(4) 47) (-2)(-1) 48) (-7)(-2) 2 0 16K uta Soft war ell C. All rights reservetr.6- Made with nfinite Algebra.
3 5 49)1--- 4 3 1 4 50) - -- 5 3 3 2 51) 1-2- 52) -1-1- 8 5 2 9 53)-1-- -- 3 5 3 5 54) - +-2-2 6 e 2016 Kuta Software LLC. All rightsreservcd:-7-madewithtnfinitc Algebra.
V. 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 59) 187(3+6-6)+1 60) (5-2) x 87 (6-2) o 20 J 6 K uta S 0 f t war ell C. A 11 rig h t s res e r v ESt. Mad e wit h n fin i tea g c bra 1.
j V. Graph each ordered pair. Label with the corresponding letter. 61) G (1,0), R (-3, 1), V (-2, -3) 62) A (3,2), B (-4, 1), C (-5, -2),! y y,s '6 k i2 x 8 14 " 2 6 x 63) F (-1-5), M (3,5), P (-4,3) 64) T (0,0), P (4, -2), S (-5, -4) y y 6 14? X 8 J6, - x 20 16K uta S 0 f t war ell C. A rig h t s res e r v e d. -G- a dew i t h Tn fin i tea g e bra.
VD. 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, -,,.71 3 2 66) '2 3 1 2-, 2.4, 2.1 2 67) 23 7! 8.4, 54 3' 2' 9 68) 714 - - 0.4, io ' 2' 5 t') 2 0 16K uta S 0 f t war ell C. All T i g h t 5 res e r v e-j 0- Mad e wit h T n fin i tea g e bra 1.
X. 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 nfinite A gebra.