Name __________________________
1-1 Essential Question: How do you evaluate algebraic expressions?
1-2/3 Essential Question: How do you add, subtract, multiply or divide signed numbers?
Fractions Essential Question: How do you add, subtract, multiply or divide fractions that do/do not have
common denominators?
1-4/5 Essential Question: What is the process for evaluating expressions containing exponents and square
roots?
How do you classify numbers within the real number system?
1-6 Essential Question: How is the order of operations used to simplify and evaluate expressions?
M11.A.1.1.1: Find the square root of an integer to the nearest tenth using either a calculator or estimation.
M11.A.1.3.1: Locate/Identify irrational numbers at the approximate location on a number line.
M11.A.1.3.2: Compare and/or order any real numbers (rational and irrational may be mixed).
M11.A.3.1.1: Simplify/Evaluate expressions using the order of operations to solve problems (any rational number may be used).
1

1-1: Evaluating and writing expressions
Variable: A letter or symbol used to represent a value that can change.
Ex:____________
Algebraic Expression: Consists of variables, numbers, and operations.
Ex: ___________
Key words for operations
______+______
______−______
______x______
______÷______
1 . Write an algebraic expression for 7 less than x : ___________________
2 . Brianna practices the piano 30 minutes each day. Write an expression for the number of hours she practices in d days. __________
3 . Maddy buys three items that cost d dollars each. She gives the cashier $10. Which expression represents the change she should receive? a.) 10 – 3d b.) 10 – d c.) 10 + 3d d.) 3d - 10
4.
Write an algebraic expression for 3 times the sum of 7 and a number y : __________
5 . Evaluate 6 – n when n = 4. __________
6 . Evaluate 3x when x = 2. ___________
2

1-2/3: Signed Numbers
Integers: The numbers (…-3, -2, -1, 0, 1, 2, 3…)
Absolute Value: How far away from zero is a number? Symbol: _____________
Rules for adding or subtracting signed numbers:
*Same signs: add the absolute values and attach the same sign.
*Different signs: subtract the absolute values, then attach the sign of the higher absolute value.
Rules for multiplying or dividing signed numbers:
*Same signs, the answer is ____________________.
*Different signs, the answer is ____________________.
Other signed number rules:
*When multiplying by 0, the answer will be ______________________.
*When 0 is divided by a number (0 is on top), the answer will be _______________________.
*When a number is divided by 0 (0 is on bottom), the answer will be ____________________.
*A minus followed by a negative equals a _____________________.
1.
-3 + 6 = _____ 2.
-7 + -4 = _____ 3.
3 – 10 = _____ 4.
-8 – (-9) = _____
5.
-6(8) = _____ 6.
(-2)(-5) = _____ 7. 5(-4) = _____ 8.

9
3
= _____
9.

12

4
= _____
0
10.
8
= _____ 11.
-8(0) = _____ 12.

0
5
= _____
13.
│-4│= _____ 14.
-│5│= _____ 15.
│-4 + -6│= ____
16.
On March 20, from 8 a.m. until 3 p.m., the temperature rose from -13ºF to 38ºF. What was the total increase in temperature during this time period?
17.
The water level of a swimming pool is 3.3 feet and changes at an average rate of -0.14 feet per day due to water evaporation. What will the water level of the pool after 4 days?
Order the numbers from least to greatest
18.
-3, -1, 4, 0, 8, -7, -9
19.
-
2
3
, -0.6, -1,
1
3
20.
│-2│, │5 - 4│, -3, │3(-1)│, -│-1│
3

ADDING/SUBTRACTING FRACTIONS
*Change all mixed numbers to improper fractions before performing the calculation.
*There must be a common denominator to +/- fractions.
*Be sure to reduce all answers.
5
1.
9
2
+
9
=
7
2.
8
5
−
9
=
3.
2
3
+ 4
5
2
3
=
5
4.
6 − 2
6
=
MULTIPLYING/DIVIDING FRACTIONS
*Change all mixed numbers to improper fractions.
*Write all whole numbers as a fraction using a “1” in the denominator.
*Multiply across the top and then across the bottom.
* When dividing, change the division sign to multiplication AND flip the second fraction. Then multiply as usual.
*Be sure to reduce all answers.
6.
2
1
3
• 3
3
4
=
5
7.
7
2
5.
7
3
•
5
=
3
÷
14
=
2
8.
6 ÷ 3
5
=
4

1-4/5: Exponents and Square Roots
__________ → 7 2 ← ________________
1.
3
2
= ______________________
3.
(
2
3
)
3
= __________________________
5.
(-6)
2
= _______________________
2.
4.
(-4)
-6
6.
5
0
2
3
= _____________________
= ______________________
= __________ (All numbers raised to
the 0 power will equal 1)
Square Root: A number that is multiplied by itself to form a product. Symbol: __________
7.
36 = _________
8.
9 = ___________
Think: _______ x ___________ = 36
\ /
identical numbers
9 .
4
25
= __________ = __________
10.

16 = _____________________
11.
Calculate each square root to the nearest hundredths place. a. √10 = b. √67 =
12.
Order from least to greatest: √12 , -3.7, 2 3
, √16 , 4.2
13.
Order from least to greatest: 0.25, 1 .
5
1
, -0.19,
5
, -0.4
Classifying numbers
Real numbers: the set of all rational and irrational numbers.
Rational numbers: numbers that either terminate or repeat.
Irrational numbers: a number that neither terminates nor repeats.
14.
Which number is irrational? Why? a.) 9 b.) 0.3333 c.) 8
2 d.)
3
5

1-6: Order of operations
from from
left to right left to right
/ \ / \
P lease E xcuse M y D ear A unt S ally
A X U I D U
R P L V D B
E O T I T
N N I D R
T E P E A
H N L C
E T Y T
S
E
S
*Parentheses include absolute values, square roots, ( ), { }, [ ], etc.
1.
12 – 3
2
+ 10 ÷ 2 • (-5) =
3.
2(-4) + 22
9 − 4
2
=
2.
4.
2 + 4[3
-3
│(-
4)
2
2
– 2(3 – 5)] =
+ 8 ÷ 2 │ =
5.
What is the value of 𝑥
2
−3𝑦
if x = 2 and y = -3?
2
6.
Mark was given the problem: “Evaluate 2x
2
+ 3 when x = 4.” He wrote that the answer was 67. Was Mark correct? Explain your answer.
6

APPLICATION OF CHAPTER 1
1.
Max needs to paint a wall that is shaped like a square. He knows that the area of the wall is 75 ft 2 . He needs to find the height of the wall. Find the height of the wall to the nearest tenth of a foot.
2.
Paula has some bricks to make a square patio. She knows she has enough bricks to cover 50 square feet.
She needs to find how long to make the patio. How long should Paula make the patio? Round your answer to the nearest tenth of a foot.
3.
Find the surface area of the rectangular prism shown. Use the expression 2lw + 2lh + 2wh.
h = 10 cm w = 8 cm
l = 12 cm
4.
The thermometer I have is in Celsius only. Today’s temperature is -20º C. What is the temperature in degrees Fahrenheit? (F =
9
5
C + 32)
5.
A fish tank is in the shape of a cube, which means each side has the same length. One of the sides measures 2 feet. What is the volume of the fish tank?
6.
Write each number as a power of the given base. a.) 16; base 2 b.) 256; base -4 c.)
8
27
; base
2
3
7