Download Ch.0 - Windsor C

Algebra I and Algebra I Concepts
Chapter 0
Section 0-2 Real Numbers
Real
Numbers
Irrational
Numbers
Rational
Numbers
Integers
Whole
Natural
Section 0-2
Square RootPerfect SquareEx. 1) Name the set(s) of numbers to which each
real number belongs.
a) 5
b)
c) 56
11
81
Section 0-2
• Graph• CoordinateEx) Graph each set of numbers on a number line
a) ì 5 , -4 , 2 , -1ü b) ìí6 4 , 49, 6.3, 57 üý c) ìí 20, 4.7, 12 , 4 1 üý
í
ý
î3 3 3 3 þ
î 5
þ
î
3
3þ
Section 0-2
Ex. 4) Simplify each square root
a) 4
b) - 49
121
256
Ex. 5) Estimate each square root to the nearest
whole number.
a) 15
b) 130
Section 0-3: Operations with Integers
What are integers?
Adding numbers with the same sign
Ex. 1)
a) 4 + 6 =
b) -4 + -6 =
Section 0-3: Using a number line or
chips to count
Number Line
1. Draw a number line and
label the numbers
2. Start at the FIRST number
listed in the problem
3. Move left if you are
subtracting, move right if
you are adding. Move the
SECOND number of spaces
Chips
1. Positive numbers are open
circles
2. Negative numbers are
closed circles
3. Draw the appropriate
circles
4. 1 open, and 1 closed circle
equal zero. Cross them off
one for one, count what is
left.
Section 0-3
Subtraction - Remember subtracting is the SAME
as adding a negative number, so
6 – 4 is the same as 6 + -4, both equal 2
*Also, subtracting a negative is the same as
addition! So, 6 - -4 is the same as 6 + 4
Ex. 2)
a) 4 – 6 =
b) -4 – 6 =
c) -4 - -6 =
d) -6 - -4 =
e) -6 – 4=
Section 0-3: Fill in the table
Problem
5+2=
5–2=
2–5=
-5 + -2 =
-5 – 2 =
-5 - -2 =
Algebraic
Number Line
Chips
Section 0-3
Multiply and Dividing Integers
Rules:
• If the numbers have the SAME SIGN, the answer is
___________
• If the numbers have DIFFERENT SIGNS, the answer
is ___________
Ex.3)
a)
b) -4 ´-5 = c) -4 ´ 5 =
d) 4 ´ -5 =
e) 4 ¸ 5 =
f)
g)
h)
Section 0-3: Fill in the table
Problem
4x5
-4 x -5
-4 x 5
4 x -5
12 ¸ 6 =
-12 ¸ -6 =
-12 ¸ 6 =
12 ¸ -6 =
Signs? (same or
different)
Sign of the answer?
Final Answer
Section 0-4: Adding and Subtracting
Rational Numbers
Ex.1) Replace the circle with < , > , or = to make
The statement true. 2
4
3
6
Ex. 2) Order the following from least to greatest
2
5
9
5
3
8
4.9
-5
3
5
Section 0-4: Adding and Subtracting
Fractions
Adding and Subtracting Like Fractions
If the ___________ are the same, add/sub the
___________. REDUCE
Ex3) Find the sum or difference
a) 3 + 1
b) 7 - 1
c) 4 - 7
5 5
16 16
9
9
Section 0-4 Adding and Subtracting
Unlike Fractions
You must have a ___________ ____________!!!
Ex.4) Find the sum or difference. Write the
fraction in its simplest form
a) 1 2
b) 3 1
c) 2 3
2
+
3
-
8 3
5
-
4
Section 0-4 Mixed Fractions
1) Turn all mixed fractions to ______________
2) Follow add/sub rules
Ex) Add/Sub the mixed fractions
a) 2 + 4 3
b) 4 5 + 2 2
c) 1 2 - 5 1
7
7
6
3
3
2
Section 0-4: Adding Decimals
1. Line up _________ points
2. Follow sign rules
Ex. 5) Add/Sub the decimals
a) 2.5 + (-3.5) b) -13.12 + (-8.6) c) -32.25 – (-42.5)
Section 0-5 Multiplying and Dividing
Rational Numbers
Multiplying Fractions
1) Change all _________ to improper
2) Multiply the _____________
3) Multiply the _____________
4) Reduce!
Ex.1) Multiply the fractions
a) 2 1
b) 3 1
c) 1 2
×
5 3
5
×1
2
×
4 9
d) -3 3
×
4 8
Section 0-5
Reciprocal –
Ex2) Find the reciprocal of the number
a) 3
b) 4
c) -7
2
8
5
9
Section 0-5
Dividing Fractions
1) Find the __________ of the second fraction
2) Follow multiplication rules
Ex 3) Find each quotient
a) 1 1 b) 3 2
c) 3 1 d) -1 -3
¸
3 2
8
¸
3
4
¸2
2
5
¸(
10
)
Section 0-6: The Percent Proportion
Ex1) Express each percent as a fraction of mixed
number. REDUCE!
a) 79%
b) 107%
c) 0.5%
Section 0-6
Percent : p (change to a decimal first!)
Whole: a
Part: b
Follow the equation ap = b
Ex2) 40% of 30 is what number?
Ex3) 67.5 is 75% of what number?
Ex4) 15 is what percent of 24?
Section 0-7: Perimeter
Perimeter –
Rectangle
Parallelogram
Square
Triangle
Section 0-7
Ex1) Find the perimeter of
each figure
a) A rectangle with a
length of 5 inches and
a width of 1 inch
b) A square with a side
length of 7 cm.
c) A parallelogram with
side lengths 12m and 14m
d) A triangle with side
lengths 4, 9, and 6 inches
Section 0-7: Circumference
Parts of a circle
Formula for Circumference
C = 2p r
Ex 2) Find the circumference
a) Radius = 4 ft.
B) Diameter = 15 cm
Section 0-8: Area
Area –
Rectangle
Parallelogram
Square
Triangle
Section 0-8: Area
Ex1) Find the area of each
figure
a) A rectangle with a length of
7 yards and width of 1 yard
d) A triangle with a base of 12
cm and a height of 5 cm
e) A circle with a radius of 3
cm
a) A square with side length of
2 meters
c) A parallelogram with a base
of 11 feet and a height of 9 feet
f) A circle with a diameter of
21 meters
Section 0-9 Volume
Volume-
Rectangular Prism
Cylinder
Section 0-9
Ex1) Find the volume
a) A rectangular prism with a
length of 8cm, width 1cm,
and height of 5 cm.
a) A rectangular prism with a
length of 4ft, width of 2ft,
and height of 3 ft.
c) A cylinder with a radius of
3in and a height of 6in
d) A cylinder with a diameter
of 10 cm, and a height of 8 cm