# Algebra 1 Summer Packet 2015

Name: _____________________________
Algebra 1
Summer Packet
2015
1|Page
Directions for Summer Packet:
1. Put your name on the packet! Do all work in PENCIL only!
2. Read each page carefully for all instructions and examples.
3. Following the examples given (or by how your last teacher
showed you), complete each problem. Show any and all work
necessary for each problem! Feel free to attach more paper is
needed (write the page number on it)
4. Calculators may be used, but try to avoid them if possible.
5. Packets will be scored during the first week of school by your
teacher.
6. Students should expect a quiz on the material in this packet,
usually the first week of school.
7. Good luck and enjoy your summer!
2|Page
Comparing Integers/Absolute Value
Use &lt;, &gt;, or = to answer the following.
1) 8
3) -5
-8
-16
5) -12
-20
2) 0
-3
4) 4
4
6) -3
4
Put the integers in ascending order.
7) 4, 5,  2, 1
8) 2,  7,  10,  3
9) 14, 12, 17 , 5
10) 3, 4 ,  2, 5
Absolute Value is the distance a number is from zero (always positive).
For example 4 = 4; 5  5
1) 2 
2) 8 
3) 5 
4) 12 
5) 21 
6) 83 
7) 100 
8) 142 
9) 231 
10) 250 
3|Page
Integer Operations
Do NOT Use a calculator on pages 4-7
*REMEMBER…
SAME SIGNS ADD AND KEEP THE SIGN
OPPOSITE SIGNS SUBTRACT AND KEEP THE SIGN OF THE BIGGEST NUMBER.
MINUS A NEGATIVE MAKE IT A BIG PLUS
1) (-12) + 7
2) (-10) + ( -7)
3) (-6) + 12
4) 8 + 7
5) 38 + (-5)
6) (-45) + 9
7) (-1) + (-46)
8) (-30) + 10
9) (-34) + 50
11) 13 + (-29)
11) 2 – (-2)
12) (-1) – 10
13) (-29)-29
14) (-8) – (-6)
15) 11 – 4
16) 48 – (-31)
17) 18 – 41
18) (-38) – 30
4|Page
More Integer Practice
1) 8+(-18)
2) -7 + (-8)
3) 26 + 6
4) -24 + 0
5) -9 + (-3)
6) -7 + 22
7) (-10) + (-13)
8) 40 + (-6)
9)
10) 19 + (-2) + (-17)
(-5) + 3 + (-17)
12) 4 – 10
13) -5 - 12
14) 3 – (-15)
15) 11 - 13
16) -7 – (-14)
17) 34- (-10)
18) -7 – (-7)
19) -7 - 7
20)
(-10) – 47 + 12 - 3
21) (-29) – 29 + (-13) – 1
22)
13 + (-29) – (-5) + 2
23)
5|Page
38 + 22 – 14 + 3
Multiplying Integers
Example: Multiplying two positive or two
negative integers gives you a positive
product.
8(7)=56
-6(-3)=18
1.
5(9)
Example: Multiplying a negative and a
positive integer gives you a negative
product.
-5(4)=-20
3(-4)=-12
2. -6(-7)
3.
7(3)
4.
5.
6(5)
6. -9(9)
7.
8(0)
8. 8(-9)
5(6)
9. -12(12)
10. -10(-46)
11. 8(-5)
12. -12(-8)
13. (-6)(-10)(-8)
14. (9)(10)(6)
15. 6 ∙ 6 ∙ -2
16. -12 ∙ 7
17. 11(-13)
18. (-7)8
6|Page
Dividing Integers
1.
Example: Dividing two positive or two
negative integers gives you a positive
quotient.
-56 / -7=8
28 &divide; 7=4
20  (5)
Example: Dividing a negative and a positive
integer gives you a negative quotient.
-21 &divide; 7= -3
36 &divide; (-9) =-4
2. 81 &divide; 9
3. -48 &divide; 8
4.
5. 0 &divide; (-12)
6. 42 &divide; (-6)
125
5
8. -96 / 12
7.
30 &divide; (-5)
9. -90 &divide; (-10)
10. -54 &divide; 3
11. -75 &divide; (-15)
12. 52 &divide; (-4)
13.
105
7
14.
4
1
15.
10
2
16.
60
15
17.
168
12
18.
7|Page
12
4
Fraction Review – ALWAYS REDUCE!!
Reducing Fractions Example
1)
12
20
2)
7
21
3)
70
105
4)
27
33
5)
63
81
6)
88
121
7)
78
112
8)
14
56
9)
105
126
10)
16
32
11)
9
21
12)
13
52
Improper Fraction to Mixed Number Example
1)
25
6
9
16
8|Page
8) 6
7
11
230
35
3)
54
3
4)
338
10
5)
75
12
6)
80
16
Mixed Number to Improper Fraction Example
7) 2
2)
9) 8
9
30
Simplify.
1)
5 3

4 4
2)
3 1

2 2
3)
2 4

5 5
4)
1 1

3 3
5)
1  5
  
3  3
6)
7 5

6 6
7)
1 1

5 5
8)
9
3

10 10
9)
3  1
  
8  3
10)
11)
9 1

8 2
13)
9 3

10 5
9|Page
9 4
 
5 3
2
14) 2   
5
15) 1
1 3

2 8
12) 3
6
1
1
7
7
 4   3
16)       
 3  2
Multiplying/Dividing Fractions and Mixed Numbers
1) 
5 1

4 3
2)
8 7

7 10
 2 5
4)    
 3 4
 1   3
5)  2    1 
 5  4
 1 7
7)    
 5 4
8) 
10) 
9
2
5
10 | P a g e
3)
4 7

9 4
 2  1 
6)  2    4 
 3   10 
1 5

2 4
9)
 4
11) 2   3 
 5
12)
1 8

2 7
1  1
 1 
9  3
Order of Operations
Use the acronym GEMDAS:
G – Grouping symbols such as parentheses, brackets, set notation, and fraction bars
E – Exponents
M/D – Multiplication &amp; division in order from left to right
A/S – Addition &amp; subtaction in order from left to right
Simplify:
2) (2)  3  5  7
3) 15  3  5  4
4) 29  3  9  4
5) 20  7  5
6) 4  9  9  7
7) 50  (17  8)
8) (12  4)  8  3
9) 12  5  6  6
10) 18  42  7
11) 3(2  7)  9  7
12) 8  22  4
1)
6  4 23
11 | P a g e
13) 16  2  5  3  6
16)
32
16  (8  2) 
14) 12  3  6  2  8  4
8  2  (3  9) 
17) 
(8  2  3)
15)
10  (27  9)
47
18) 6  5  56  7  7  2
Evaluating Expressions
Evaluate = plug in for the variable and simplify
Example: given x = 2 and y = 4, evaluate 3x + y
SOLUTION = 3(2) + (4) = 6 + 4 = 10
Evaluate each expression given that x = 5, y = -4, and z = 6
1) 3x - z
2) yz + 4
3) 2xy + z
4) 2(x + z) – y
5) 4y – 5z + 1
6) -2xyz + x
12 | P a g e
MORE PRACTICE — Evaluate each expression given that a=2, b=3, c=6, and d=12.
1) (a  d )  (b  c )
Example
2)
d
a
3) b 2
4)
c
 2b
a
5) 3a 2  d
6) cd  ab
7) bc  d
8) 3d  a 2  b
10)
13)
9)
a  b c d
12)
ab
cd
14)
15) c  a  d
2
13 | P a g e
2
16)
bc
d
a
d
a
c
2a  3a  a
(a  b  c  d )0
Combining Like Terms
Example
1) 5y  y
2) x  4x
3) 3a  2a
1
4) m  m
2
5) 11x  3y  5x
6) 6y  3z  3y
7) 13a  13b  13c  15a
8) 6p  2p  18
9)
2
3
1
2
y x y x
5
5
5
5
10)
17a  18b  20b  a
11) 5  3x  2x + 55
12)
27 + 3x  4x  6x + 4
13)
14 | P a g e
8(5b  7)  5b
Example:
1) n  28  84
2) x  48  129
3) y  59  194
4) b  48  190
5) p  167  75
6) r  46  278
7) x  87  364
8) a  76  69
15 | P a g e
Multiplication &amp; Division Equations
Example:
1) 2y  98
3)
b
6
22
5) 33 
y
16
7) 432  36a
16 | P a g e
2) 7x  168
4)
x
9
2
6) 27m  972
8) 84 
m
4
9)
c  15  10
10) a  57  60
11) 2x  86
12)
y  28  28
13) 42  p  (25)
14)
x  45
15)
y  ( 12)  49
16) 4 p  112
17)
b
7
6
18)
17 | P a g e
x
 6
5
TWO STEP EQUATIONS
Example
1) 7y  9  72
2) 4x  6  38
3) 7a  2  47
4) 5m  4  51
5) 3x  9  24
18 | P a g e
6)
x
 4  4
6
7)
x
 10  13
8
8) 8c  3  69
9) 49  7(y  7)
10) 18  3y  57
11) 3p  5  37
12) 6x  3  9
14)
x
 10  15
3
19 | P a g e
13)
x
42
7
15) 2x  11  9
Proportions:
REMEMBER, CROSS MULTIPLY!
1)
4 2

9 x
2)
6 3

a 8
3)
8n 8

8
3
4)
7 a

9 5
5)
p 13

8 2
6)
3 x

13 3
7)
10 2

12 n
8)
9 x

7 14
9)
x 4

9 6
10)
x 10

12 2
20 | P a g e
11)
6
5

14 x
12)
3x
6

5
10
Writing Algebraic Expressions
Example
1) 5 more than x
2) C less than 5
4) The product of 3 and h
5) Half of y
6) Three times a number
7) A number increased by three times y
8) A number y increased by itself
9) Three less than twice y
10) 2 more than the product of 6 and y
11) The quotient of a number divided by 10
12) The perimeter of a square with sides length x
13) 5 more than 2 times a number
14) 2 diminished by 7 times a number
15) Twice a number, decreased by 7
16) One-fourth of a number
17) 9 times a number, increased by 4 times
the number
18) 8 times the sum of a number and 3
19) 3 times the sum of twice a number and 8
20) Two-thirds of a number
21) 10 meters higher than height x
21 | P a g e
Properties:
Match the following properties to their example.
(note: some may be used more than once and some not all)
H. Identity of Multiplication
J. Inverse of Multiplication
K. Distributive
L. Multiplication of Zero
F. Commutative of Multiplication
M. Multiplication of -1
G. Associative of Multiplication
______13.
(4  5)  2  4  (5  2)
_______2.
1
1
7
1(5)  5
______14.
19  0  19
_______3.
8 4  2  8 2  4
______15.
15(1)  15
_______4.
47 6  7 64
______16.
4  11  11  4
_______5.
4  7  4  x  4(7  x )
______17.
6 92  2 9 6
_______6.
(a  b )7  7(a  b )
______18.
1  23  23
_______7.
(3  2)  1  3  (2  1)
_______19.
2 3
 1
3 2
_______8.
70  0
_______20.
3x   1  3x
_______9.
53   53  0
_______21.
25  0  4  0
_______10.
80 8
_______22.
1  0  1
_______11.
(4  7)  3  4  (7  3)
_______23.
9(x  3)  9x  27
_______12.
2(x  3)  2x  6
_______24.
x  (x )  0
_______1.
22 | P a g e
7
2
2