Morrisacademy for Collaborative Studies

Unit One: Real NumbersName: ______

Flay y Nunez

MorrisAcademy for Collaborative Studies

Ms. Flay and Mr. Nunez

Algebra I

Unit One: Real Numbers

Name:______

Addition/Subtraction of Signed Numbers

Addition of Signed Numbers

Signed Numbers = all numbers.

What do I mean by Signed ?

______.

Addition Rules:

1. Same Signs: keep signs and add

ex. –3 + –2 = -5

2. Different Signs: take sign of bigger number then take difference.

ex. -3 + 2 = -1

Unit One: Real NumbersName: ______

Flay y Nunez

Examples-

Directions: Find the solution.

1. 2 + -9 = / 2. -5+-3 =
3. 8+6 = / 4. -8+-6 =
5. -8 + 4 + -10 + -2 + 3 = / 6. -4 + -2 =

Unit One: Real NumbersName: ______

Flay y Nunez

Subtraction of Signed Numbers

How would you do this problem?

Change from subtraction

to addition.

Change sign of second number.
Add.

Unit One: Real NumbersName: ______

Flay y Nunez

Examples-

Directions: Find the solution.

Unit One: Real NumbersName: ______

Flay y Nunez

1. 3 – (-9) = / 2. -2 - -4 =
3. -5 - 4 = / 4. -3 – (-2 – -6) =
5. -3 – 0 = / 6. 0 – 3 =

Unit One: Real NumbersName: ______

Flay y Nunez

Now find the solutions with the calculator. Check your answers above.

1. 3 – (-9) = / 2. -2 - -4 =
3. -5 - 4 = / 4. -3 – (-2 – -6) =
5. -3 – 0 = / 6. 0 – 3 =

QUIZZES

AddingName______

7 + 6 / -14 + 9 / -5 + -6
-18 + -5 / -6 + (13) / 4 + -12
a = -3; b = 0; c = 5 / c + (-a) / (-b) + c + a

SubtractingName______

3 – 6 / -2 – (-3) / -5 – -2
-5 – (-2) / -4 – 8 / 10-3
x = 1; y = 2; z = -3 / x + y – z / y – (x + z)

Multiplication and Division

of Signed Numbers

METHOD 1:

1. 2(3) = 3. 2(-3) =

2. -2(-3)= 4. -2(3)=

Unit One: Real NumbersName: ______

Flay y Nunez

Method 2: Triangle Trick

__ __

Directions: Use your preferred method to solve the following problems.

1. 0(-3) = / 4. 18(-3) =
2. 12(4) = / 5. -15(6) =
3. -13(-5) = / 6. -9(1) =

Exponents and Multiplication

1. (-2)3 =

-2 • -2 • -2 =

4 • -2 =

2. (-3)4 =

-3 • -3 • -3 • -3 =

9 • 9 =

ODD exponents with Negative Base – NEGATIVE Product
EVEN exponents with Negative Base –

POSITIVE Product

Unit One: Real NumbersName: ______

Flay y Nunez

Division of Signed Numbers

__ __

Directions: Use your preferred method to solve the following problems.

1. / 6.
2. / 7.
3. / 8.
4. / 9.
5. / 10.

Unit One: Real Numbers Name:______

Flay y Nunez

QUIZ

Multiplying and Dividing Real Numbers

Directions: solve the following problems.

(-4)(5) / 24  (-6) / -2  8
-63  -9 / (-4)(-4)(-4) / -2/3 3/2
–8(-5)
-4 / -3/5  (-3/4) / -9 + -6
-3

The Real Numbers

Counting Numbers

1,2,3,4….

Whole Numbers

0,1,2,3,4….

Integers

…-4,-3,-2,-1,0,1,2,3,4….

Rational Numbers

...-4,-3,, -2, -1,, 0, , 1,2, 2, 3, 3.8,4...

Irrational Numbers

……

Real Numbers

...-4,-3,, -2, , -1,, 0, , 1, , 2, 2, 3, , 3.8,4...

What am I?

Directions: Classify each number by checking the appropriate category. A number could belong to more than one category.

Number / Natural / Whole / Integer / Rational / Irrational
-25
¼
1.54
.11111…
49
53
0


Calculator Craziness

Number / Decimal
round to 4 places / Type of decimal / Type of Number
1.
2.
3.
4. 10.5476
5. 2
6.
7. -4
8. 0
9. 84.5559
10.

Rational Versus Irrational

Rational / Irrational

Prime Numbers Versus Composite

Prime Numbers- a number greater than 1that has no other factors but itself and 1.

Examples- 2,3,5,7,11,13,17

___ x ___ = 2?

___ x ___ = 5?

___ x ___=12?

Are there any more factors of 12?

Composite Numbers-numbers that are NOTprime. 12 is a composite number.

Other Examples of Composite Numbers-

Exponents and Square Roots

Exponents

Bases, Exponents, and Powers

The exponent 3 indicates that the base is used 3 times.

4 x 4 x 4 = 64

Examples

Write the following examples in standard form.

Write the following examples in exponential form.

4. 5 x 5 x 5 x 5 =

3 x 3=

Square Roots and Other Roots

Why is the square root of a number related to exponents?

Examples-

Exponents and Roots Worksheet

Square Root Fun

Find the square root of the following problems. Round decimal to 4 places.

1. / 6.
2. / 7.
3. / 8.
4. / 9.
5. / 10.

Real Numbers: Group Activity

In your groups you will be given 4 cards, each card has a number on it. Your task is to:

1)Find the decimal value of each number using your calculator

2)Order the numbers from least to greatest.

Below is space to help you organize your work.

1st Number: ____ = ______

2nd Number: ____ = ______

3rd Number: ____ = ______

4th Number: ____ = ______

Now you have to order the numbers from least to greatest.

leastgreatest

______

Let the calculator go to work for you…

1
*Regents* / Kyoko’s mathematics teacher gave her the accompanying cards and asked her to arrange the cards in order from least to greatest. In what order should Kyoko arrange the cards?

=
=
=
=
=
2
*Regents* / In which list are the numbers in order from least to greatest?
(1) (3)
(2) (4)
3
*Regents* / Which numbers are arranged from smallest to largest?
(1) (3)
(2) (4)
4
*Regents* / Which list is in order from smallest value to largest value?
(1) (3)
(2) (4)
5
*Regents* / Which expression has the smallest value?
(1) (3)
(2) (4) –3.02

Order of Operations

What do I mean by operation?

What are parentheses?

What is an exponent?

Simplify Numerical Expressions:

Do inside ______.

Get rid of ______.

Do all ______and ______from left to right.

Do all ______and ______from left to right.

What Is the Order of Operations?

Examples

1. / 2.
3. / 4.

What Is the Order of Operations?

Let’s Try a Few More…

1. / 2.
3. / 4.
5. / 6.

Order of Operations-Advanced

Directions: Complete the following problems.

1. 15 – 3(4) = / 2.
3. / 4.
5. 12 + 2 - 2(2 + 3)= / 6.
7. / 8. *Regents* What is the first step in simplifying the expression
(1) square 5 (3) subtract 3 from 2
(2) add 4 and 5 (4) multiply 3 by 4
9. *Regents* The expression
15 – 3[2 + 6(–3)]
simplifies to
(1) –45 (3) 63
(2) –33 (4) 192 / 10.

Properties of Operations

Commutative Property

5 + 8 = 13

8 + 5 =

7 x 4 = 28

4 x 7 =

Associative Property

(1 + 2) + 3 = 6

1 + (2 + 3) =

(1 x 2) x 4 = 8

1 x (2 x 4) =

Distributive Property

2(3 + 5) = (2 x 3) + (2 x 5)

2(3 + 5) =(2 x 3) + (2 x 5)=

Examples-

4(2 + 3) =

3(4 + 2) =

Directions: Answer the questions below.

6
Regents / The equation *(∆ + ♥) = *∆ + *♥ is an example of the
(1) associative law (3) distributive law
(2) commuative law (4) transitive law
7
Regents / Which equation illustrates the distributive property?
(1) 5(a + b) = 5a + 5b(3) a + (b + c) = (a + b) + c
(2) a + b = b + a (4) a + 0 = a
8
Regents / If M and A represent integers, is an example of
which property?
(1) commutative (3) distributive
(2) associative (4) closure
9
Regents / Which expression is an example of the associative property?
(1) (x + y) + z = x + (y + z)
(2) x + y + z = z + y + x
(3) x(y + z) = xy + xz
(4) x • 1 = x
10
Regents / Which equation illustrates the associative property of addition?
(1) x + y = y + x (3) (3 + x) + y= 3 + (x + y)
(2) 3(x+ 2) = 3x+ 6 (4) 3 + x= 0

Additive Identity

Any number ______to ______is itself.

2 + 0 = 2

7 + 0 = 7

-3 + 0 = -3

Additive Inverse (OPPOSITE)

Any number added to its additive inverse(opposite) is ZERO.

4 + (-4) = 0

9 + ___ = 0

Multiplicative Identity

6 x 1 = 6

-3 x 1 = -3

4 x 1 = 4

Any number ______by one is that ______.

Multiplicative Inverse (RECIPROCAL)

Any number multiplied by its reciprocal is ______.

Zero Product Property

8 x 0 = 04 x 0 = 0

Any number multiplied by zero is ______.

Closure Property

A______is CLOSED under an operation ( ) when a pair of ______under a given ______yields an element in

the ______set.

Examples-

23 + 11 = 34  whole number +______= whole number

7.8 + 4.8 = 12.6  ______+ rational number = rational number

 ______- irrational = ______!!!!

Directions: Answer the questions below.

11
Regents / Which property is illustrated by the equation
(1) commutative property of addition
(2) distributive property
(3) additive inverse property
(4) additive identity property
12
Regents / Which equation is an illustration of the additive identity property?
(1) x • 1 = x (3) x – x = 0
(2) x + 0 = x (4)
13
Regents / Which statement best illustrates the additive identity property?
(1) 6 + 2 = 2 + 6 (3) 6 + (-6) = 0
(2) 6(2) = 2(6) (4) 6 + 0 = 6
14
Regents / Which equation illustrates the multiplicative identity element?
(1) x+ 0 = x (3)
(2) x– x= 0 (4)
15
Regents / What is the additive inverse of
(1) (3)
(2) (4)
16
Regents / Which property of real numbers is illustrated by the equation
(1) additive identity
(2) commutative property of addition
(3) associative property of addition
(4) additive inverse

Unit One: Real Numbers Name:______

Flay y Nunez

Absolute Values

The Absolute Value of a number is its distance from zero.

1. / 2.
3. / 4.
5. / 6.
7. / 8.
9. / 10.