7th Grade Math

Number System

Day 1Number System,

Opposites &Absolute Value

Number System

0.22

Natural1,2,3...

Whole

0

Integer

...-4, -3, -2, -1

Rational

1/5

5/2

8.3

-2.756

-3/4

1/3

-1/11

Real

Irrational

{...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...}

Definition of Integer:

The set of whole numbers, their opposites and zero.

Define Integer

Examples of Integer:

X

Definition of Rational:

A number that can be written as a simple fraction

(Set of integers and decimals that repeat or terminate)

Define Rational

0, -5, 8, 0.44, -0.23,

Examples of rational numbers:

9 , ½

X

Definition of Irrational:

A real number that cannot be written as a simple fraction

Define Irrational

Examples of irrational numbers:

X

Rational and IrrationalPerfect Squares: Rational

Imperfect Squares: Irrational

Terminating Decimals (3.89) and Repeating Decimals ( ) are rational.

Rational & Irrational Numbers

is rational because the radicand (number under the radical) is a perfect square

If a radicand is not a perfect square, the root is said to be irrational.

Ex:

Perfect Square – a number multiplied by itself. Ex: 82, 102, 132

Square Root – also called radical. a number that is multiplied by itself to form a product called a square.

Imperfect Square Root – a radical whose square root is not a whole number. Ex:

Changing a Repeating Decimal to a Fraction

to a fraction n =

Multiply both sides by 100. 100n = (100)

100n = 45. Subtract n from both sides. -n - _________________ 99n = 45Divide both sides by 99. __________________ n = 45/99

n = 5/11

Natural Numbers:

Whole Numbers:

Additive Inverse:

integer rational irrational

Classify each number as specific as possible: Integer, Rational or Irrational

5

-6

0

-21

-65

13.2

-6.32

9

2.34437 x 103

½

¾

3¾π5

-1 0-2-3-4-5 1 2 3 4 5

Rational Numbers on a Number Line

NegativeNumbers

PositiveNumbers

Numbers to the left of zero are less than zero

Numbers to the right of zero are greater than zero

Zero is neitherpositive or negative

Zero

2 Which of the following are examples of integers?

A

B

C

D

E

-5

0

-3.2

12 1 2

3 Which of the following are examples of rational numbers?

A

B

C

D

E

13

-3

10

0.25

75%

Numbers In Our World

You might hear "And the quarterback is sacked for a loss of 5 yards."

This can be represented as an integer: -5

Or, "The total snow fall this year has been 6 inches more than normal."

This can be represented as an integer: +6 or 6

Numbers can represent everyday situations

1. Spending $6.75

2. Gain of 11 pounds

3. Depositing $700

4. 10 degrees below zero

5. 8 strokes under par (par = 0)

6. feet above sea level

Write a number to represent each situation:

4 Which of the following numbers best represents the following scenario:

The effect on your wallet when you spend $10.25.

A

B

C

D

-10.25

10.25

0

+/- 10.25

5 Which of the following integers best represents the following scenario:

Earning $50 shoveling snow.

A

B

C

D

-50

50

0

+/- 50

6 Which of the following numbers best represents the following scenario:

You dive feet to explore a sunken ship.

A

B

C

D

0

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

The numbers -4 and 4 are shown on the number line.

Both numbers are 4 units from 0, but 4 is to the right of 0 and -4 is to the left of zero.

The numbers -4 and 4 are opposites.

Opposites are two numbers which are the same distance from zero.

Opposites

7 What is the opposite of -7?

8 What is the opposite of 18.2?

What happens when you add two opposites?

Try it and see...

A number and its opposite have a sum of zero.

Numbers and their opposites are called additive inverses.Click to Reveal

• An integer is a whole number, zero or its opposite.

• A rational number is a number that can be written as a simple fraction.

• An irrational number is a number that cannot be written as a simple fraction.

• Number lines have negative numbers to the left of zero and then positive numbers to the right.

• Zero is neither positive nor negative.

• Numbers can represent real life situations.

To Review

X

Absolute Value of Numbers

The absolute value is the distance a number is from zero on the number line, regardless of direction.

Distance and absolute value are always non-negative (positive or zero).

10 2 3 4 5 6 7 8 9 10-1-2

-3-4-5-6-7-8-9-10

What is the distance from 0 to 5?

10 2 3 4 5 6 7 8 9 10-1

-2-3-4-5-6-7-8-9-10

What is the distance from 0 to -5?

10 2 3 4 5 6 7 8 9 10

-1-2

-3

-4

-5-6-7

-8

-9

-10

Absolute value is symbolized by two vertical bars

|4|

What is the | 4 | ?

This is read, "the absolute value of 4"

|-4| = 4

|-9| = 9

= 9.6|9.6|

Use the number line to find absolute value.

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

Moveto check

Move to

check

Moveto check

14 Find

15 Find |-8|

Treat Absolute Value Symbols as parenthesis.

Examples: a)

b)

c)

17 What is ?

18 Find

A

B

C

D

E

-30

-15

0

15

30

20 Which numbers have 15 as their absolute value?

A

B

C

D

E

-100

-50

0

50

100

21 Which numbers have 100 as their absolute value?