Drill #14

State the hypothesis and conclusion of each statement. Determine whether a valid conclusion follows from the statement. If not give a counterexample.

1. If two numbers are odd their difference is even.

2. The quotient of two even numbers is even.

3. If a number is prime then it must be odd.

Drill #15

1-8 Study Guide

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1-8 Number Systems

Objective: To classify and graph real numbers, and to find square roots and order real numbers.

Open books to page 46.

Number Sets (Vocab)

Real Numbers (R)

Rational Numbers (Q) Irrational Numbers (I)

• Integers (Z)– Whole Numbers (W)

• Natural Numbers (N)

(1). Venn Diagram for Real Numbers *

Reals, R

I = irrationals

Q = rationals

Z = integers

W = wholes

N = naturals

I QZ

WN

(38.) Real Numbers **R

Definition: The set of all rational and irrational numbers. ALL numbers are real numbers.

5 ¼ 1.76324323213223134123

6 0.5 -63 1.76 pi 1.3333333

-10 1,000,000,000 -32.65

Rational and Irrational numbers** Q I

(39.) Irrational Numbers: Any number that is not rational. (all non-terminating, non-repeating decimals)

Examples:

(40.) Rational numbers: a number that can be expressed as m/n, where m and n are integers and n is not zero. All terminating or repeating decimals and all fractions are rational numbers.

Examples: 8.5,34.1,9,3

1

7,,2

(41.) Natural Numbers**N

Definition: The set of counting numbers, starting at 1, and including all the positive whole numbers. {1, 2, 3, 4, 5, 6, 7, 8, 9, … }

‘…’ means that it continues on to infinity.

The natural numbers are a set of numbers.

(42.) Whole Numbers**

Definition: The set of numbers that includes all the Natural numbers, and 0.

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, … }

What is the difference between Natural numbers and Whole numbers?

Is 0 a natural number? Is 0 positive or negative?

(43.) Integers**Z

Definition: The set of numbers that includes all the Whole numbers and all the negative Natural numbers.

{ …, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, …}

The set of integers starts at negative infinity, and counts by ones all the way to positive infinity.

Example 1*

Name the sets of numbers to which each number belongs:

56.

81.

22

5.

c

b

a

Graph and Coordinate **

44. Graph: To plot a point on number line.

45. Coordinate: The number that corresponds to a point on a number line.

Name the coordinate of the point that is graphed on the number line below.

-2 -1 0 1 2-3

Graphing inequalities*• Plot the constant (the number on the opposite

side of the inequality) on the number line.• < and > get open circles • < and > get closed circles• For > and > the graph goes to the right. (if the variable is on the left-hand side)• For < and < the graph goes to the left. (if the variable is on the left-hand side)

Example: 1-8 Skills Practice #13x > -1.

Example 3*

Graph each set of numbers:

5.4.

2.

}3

5,3

2,3

1,3

4{.

ac

xb

a

(46.) Square Root **

Definition: If then x is a square root of y.

NOTE: Once the square root is evaluated, the radical is removed.

Examples:

yx 2

xy

39 525

(47.) Perfect Squares **

Perfect Squares:

Definition: Perfect squares are numbers that have whole number square roots.

NOTE: The area of squares with integer length sides are perfect squares.

14

916

2536

49

Evaluating Square Roots*

Principal Square Root

Negative Square Root

Both Roots

NOTE: The radical is removed after you evaluate the root.

864

864

864

Squares Table x

1 1 11 121

2 4 12 144

3 9 13 169

4 16 14 196

5 25 15 225

6 36 16 256

7 49 17 289

8 64 18 324

9 81 19 361

10 100 20 400

2x2x2x

Example 4*

Find each square root:

69.1.1121

4.1

256

49

BA

(48.) Rational Approximation**

Definition: A rational number that is close to, but not equal to, the value of an irrational number.

Example:

NOTE: Use rational approximations to order numbers

41.12

Examples

1-8 Study Guide

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