PRE-ALGEBRASummer Packet
VANDEBILT CATHOLIC HIGH SCHOOLIncoming 8th Grade
EXAMPLES
Section I
Objective: Write an algebraic expression to represent unknown quantities with one unknownand 1 or 2 operations
Examples:The examples below show algebraic expressions written as mathematical expressions.
9 more than a numberthe sum of 9 and a numbera number plus 9a number increased by 9the total of x and 9
x+9
4 subtracted from a numbera number minus 44 less than a numbera number decreased by 4the difference of hand 4
h-4
6 multiplied by 96 times a numberthe product of 9 and 6
6g
a number divided by 5
the quotient of t and 5
divide a number by 5
t5
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 performingindicated operations.
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 III
Objective: Solving equations for missing variables
Examples:The examples below show how to solve equations using addition, subtraction, multiplication,and division.
2x = 2 Isolate x
2x + 5 = 7 Use inverse operations to isolate the variable
-5 -5 Subtract 5 from both sides
+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 Isolate x
Divide 6 on both sides
x=4
Section IV
Objective: Solving proportions
Examples:The examples below show how to solve proportions by cross multiplication.
x 24
12 3Cross multiply to solve for the missing value
12 x 24 = 3 x x Multiplication
288 = 3x Isolate x
-;- 3 -;- 3 Divide 3 on both sides
x = 96
X 14=2 7Cross multiply to solve for the missing value
2 x 14 = 7 x x Multiplication
28 = 7x Isolate x
-;-7 -;-7 Divide 7 on both sides
x=4
Section V
Objective: Performing operations with negative integers
Examples:The examples below show how to perform operations with negative integers. These are justsome 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
Examples:Rational Numbers: Helpful processes and tips
Multiplying Fractions and Mixed Numbers1. 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 numbers1. Change any mixed number to an improper fraction
2. Keep the first fraction, change the division sign to a multiplication sign and flip the secondfraction 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 Numbers1. Change any mixed number to an improper fraction
2. Find common denominators3. 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 (left to right)
Addition &5 ubtraction (left to right)
4 + 24 -i- 4 Division
(3 + 1) + (4 x 6) -;-4 Do what's inside of the parenthesis
4+6 Add
= 10
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-Y I
I -Quadrant II Quadrant!
(-, +) (+,+)
2
-s 0 sx
Quadrant Ilf-2
Quadrant IV(-, -) (+, -)
-s
r..E.•
..
'. /J.
:;.~
~ .,
- '}
f',.,.;
c
-,
Graphing Ordered Pairs:
1. We move along the x-axis first2. Move along the y-axis second3. Plot the point and label with the given variable
B•
c•
Graph the following ordered pairs:
A (1,3)
B (3,1)
C (3,-3)
D (-4,2)
E (-1,5)
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 togreatest.
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 0 1 2 3 4 5 6 7 8 9 10
negative zero positive
Order the rational numbers from least to greatest:14 6 320} 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
< I : I + I II I I I I t I I-1
0.3 0.7I /I t I I I + Io
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 geometricfigures.
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
Parallelogram: P = 51 + 52 + 53 + 54 A = bh
Formulas
Rectangle: P = 21 + 2w A = lw
Square: P = 45
Triangle: P = 51 + 52 + 53 A = !bh2
Trapezoid: P = 51 + 52 + 53 + 54
Circle: Circumference = ttd
PRE-ALGEBRA VANDEBILT CATHOLIC mGH SCHOOL© 2016 Kuta Software LLC. All rights reserve d.
Summer Packet Incoming 8th grade
Please show your work for all problems given. Make sure you BOX off your answers. Pleaserefer to the example problems attached to the packet if you have any questions or need anyguidance.
I. Write each as an algebraic expression when given as a verbal expression and as a verbalexpression 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
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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
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III. Solve each equation given.
15) v- 5 =-4
x17) 4=- 20
19) 36 = 17+ x
21) -3 = a - 19
23) 15= -5n
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16) 2 = a-7
a18) -= -16
19
20) 13=-4+b
x22) 3=-
12
24) -2=x+ 13
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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
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IV. Solve each proportion.
9 235) x 4
4 936) -=-
m 6
5 m37) -=-
10 9v 538) -=-2 6
9 x39) -=-8 3
40) !=~n 3
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V. Operation practice with negatives
41) 909
42) -35-7
43) Q-4
44) 90-9
45) (-9)(-10) 46) (-6)(4)
47) (-2)(-1) 48) (-7)(-2)
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3 549)1---
4 31 450) - --5 3
351) 1- 2-
82
52) -1-1-5
2 953)-1-- --3 5
3 554) - +-2-2 6
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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
59) 187(3+6-6)+1 60) (5 - 2) x 87 (6 - 2)
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VII. 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
j I ,!
I,Is '6 k i2 xI
y
I I8 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
I
I I6 14 ? X
II
y
I
8 J6 ,x-
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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.
2 565) 1.4, -, ,.713 2
66) '23
12-, 2.4, 2.12
67) 23 7! 8.4, 543' 2' 9
68)714- - 0.4,io ' 2' 5
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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 aheight 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.