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

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

x17) 4=- 20

19) 36 = 17+ x

21) -3 = a - 19

23) 15= -5n

© 2016 Kuta Software LLC.

16) 2 = a-7

a18) -= -16

19

20) 13=-4+b

x22) 3=-

12

24) -2=x+ 13

All rig h t s res e r v e d -:-3- Mad c wit 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 - 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.