Study Guide
Unit 1: Variables, Expressions, and Integers
Quiz 1A:
1.1 Expressions & Variables
1.2 Powers & Exponents
1.3 Order of Operations
1.4 Compare & Order Integers
1.5 Adding Integers
1.6 Subtracting Integers
1.7 Multiplying & Dividing Integers
Quiz 1B:
2.2 Simplify Expressions: Distributive Property
2.3 Simplify Expressions: Combine Like Terms
Unit 1 Test on all of the above topics
*For more practice and test preparation:
1) Online textbook: http://www.classzone.com/eservices
*Email Ms. Botto or Mr. Bovee if you forgot the activation code.
2) IXL.com links on Ms.Botto’s webpage
3) Review class notes, classwork, and homework assignments.
Notes, sample problems, and vocabulary
for each skill are in the following pages.
1.1 Expressions & Variables
Expression: consists of numbers and operations, and sometimes variables. (Examples: x-4 and 3x+b)
Variable: a letter to represent one or more numbers.

1)
3)
Evaluate the expression if x = 3 and y = 5.
x+7
x+y
10
2)
4y
8
4)
xy
20
15
 Write a Variable Expression.
1) The difference of 8 and a number
8-x
2) The quotient of a number and 5
a ÷ 5 or
3) 10 less than a number
𝑎
5
x – 10
4) The product of 3 and some number
3x
Some Common Operation Words
Addition Words
Subtraction Words
sum
more than
in total
plus…
difference
less than
decreased by…
Multiplication Words
Division Words
product
times
multiplied by
twice (times 2)
doubled (times 2)
quotient
divided by
into…
half (divided by 2)
1.2 Powers & Exponents
53 = 125
power: the result of repeated multiplication of the same number.
base: a letter to represent one or more numbers
exponent: a letter to represent one or more numbers

Write the product using an exponent.
1)
13  13  13  13
3)
xxxxxx
134
2)
x6
4)
mm
2)
y3
(0.2)(0.2)(0.2)
(0.2)3
m2
 Evaluate the expression when y = 3.
1)
y2
9
( 3  3 = 9)
27
( 3  3  3 = 27)
 Find the area of the square with the given side length.
1)
9 meters
92 = 81 m2
2)
11 inches
112 = 121 in2
1.3 Order of Operations
PEMDAS
Grouping Symbols
(Parentheses, brackets, etc.)
a)
(10 – 5) – 2
b)
(5) – 2 =
10 – (5 – 2)
3
10 – (3) =
7
Exponents
a)
2 + 32
2+9=
2 2 + 32
b)
11
4+9=
13
Multiply OR divide
In order from left to right!
a)
10 ÷ 5 ● 4
b)
2 4=
24
3
● 2
82=
8
c) 5 ( 7 – 3 ) ÷ 2
16
5 (4) ÷ 2
20 ÷ 2 =
Subtract OR add
In order from left to right!
a)
10 – 6 + 3
4+3=

1)
b)
7
10 + 6 – 3
16 – 3 =
13
Evaluate the expression when x = 4 and y = 2.
3x – 2y
3 ( 4) – 2(2)
12 – 4 =
2)
8
x2 – y
42 – 2
16 – 2 =
14
10
1.4 Comparing & Ordering Integers
Integers: all of the counting numbers, their opposites, and zero.
Absolute Value: a numbers distance from zero.
Opposites: the same value but different sign.

Order these integers from least to greatest: -8, 5, -4, 2, 0, 6
You can use a number line to order integers.
Answer: -8, -4, 0, 2, 4, 6

State the absolute value of the number.
1) 5

5
12
2) - 15
15
State the opposite of the number.
1) 6

2) - 12
-6
Evaluate the expression when y = -5.
1) -y
5
- (-5) = 5
2) 17 - y
17 - 5
12
1.5 Adding Integers
(To the tune of Row, Row, Row Your Boat)
Same sign keep and add
Different signs subtract
Take the sign of the higher number,
Then you’ll be exact!

Find the sum.
1)
-11 + 6
-5
2)
-1 + (-8)
-9
3) 52 + (-30) + (-46)
22 + (-46) = -24

Evaluate the expression when x = -22 and y = -12.
1)
x + (-9)
-22 + (-9) =
2)
-31
x + 17 + y
(-22) + 17 + (-12)
-5 + (-12) =
-17
-24
1.6 Subtracting Integers
(To the Aretha Franklin’s Chain of Fools)
Keep Change Change
(Change the subtraction sign to addition, then change the following number’s sing. Follow adding integers rule.)

Find the difference.
1)
4 – 10
4 + -10 =
2)
-6

Evaluate the expression when x = -9.
1)
x – (-40)
( -9) + 40 =
7+5=
3)
12
31
Find the change in temperature.
1)
From 32˚ F to -10˚ F
42˚F
-2 – (-9)
-2 + 9 =
2)

32 – (-10)
32 + 10 =
7 – (-5)
7–x
7 + (9) =
2)
16
From -45˚F to -80˚F
-45 – (-80)
-45 + 80 =
35˚F
7
1.7 Multiplying & Dividing Integers
+
-
+
-
+
IF the signs are the same, the product/quotient is positive.
If the signs are different, the product/quotient is negative.

Find the product or quotient.
1)
9 (-11)
3)
−24
3
-99
-8
2)
4)
-6 (-8)
−16
−4
48
4
2.2 (Simplifying Variable Expressions) Distributive Property

Use the distributive property to write an equivalent variable expression (simplify the expression).
1)
3 (x + 7)
+

3x + 21
(x+7)
(x+7)
(x+7)
3x + 21
2)
OR
3 (x) + 3(7) = 3x + 21
( n + 4) -2
-2n – 8
( n + 4) OR -2 (n) + -2 (4) = -2n – 8
( n + 4)
2n + 8, apply the negative: -2n – 8
+
Find the area of the rectangle or triangle.
2
2y + 1
3x – 8
16
*Area of a rectangle is length times width.
So set up an expression like this:
Area of a triangle is length times width divided by 2.
So set up an expression like this:
1)
2)
2 ( 3x – 8 ) =
6x - 16
16 ( 2y + 1 )
2
=
32y + 16
2
= 16y + 8
2.3 (Simplifying Variable Expressions) Combining Like Terms
4x2 + 2 + 3x2 – 1 + x
Terms: the parts of an expression; includes constants, variables, and coefficients.
*In the expression above, the terms are: 4x2, 2, 3x2, -1, and x
Constants: a number that has no variable.
*In the expression above, the constants are: 2 and -1
Coefficients: the number that multiplies a variable.
*In the expression above, the coefficients are: 4, 3 and 1 (1 because there is 1x, even if 1 is not written there.)
Like Terms: the terms in an expression that “match”.
*In the expression above, the like terms are: 4x2 and 3x2; 2 and -1
(x does not have a like term with any other constant.)

Simplify the expression.
*Circle or box the like terms!! Include the sign IN FRONT!!
*Follow integer rules!
1) 17x2 + 2 + x2 – 5 =
19x2 – 3
2) 3x – 21 – 7x + 20 =
3) 5 ( x – 2 ) – 9x + 11 =
-4x + 1
4) 6x – ( 8 – 14x ) + 1 =
*Distribute before combining like terms:
5x – 10 – 9x + 11 = -4x + 1
-4x – 1
20x – 7
*Watch for a negative outside of parentheses:
Distribute a -1 to terms inside the parentheses:
-1 ( 8 – 14x ) = -8 + 14x
6x – 8 + 14x + 1 = 20x – 7