Properties of Real Numbers

Presentation

•

Mathematics

•

Professional Development

•

Hard

Joseph Anderson

FREE Resource

10 Slides • 20 Questions

The Properties of Real Numbers

by Dr. Luis Bello

We have already described numbers as counting numbers, whole numbers, and integers. Do you remember what the difference is among these types of numbers?

Do you remember what the difference is among these types of numbers?

counting numbers 1,2,3,4…

whole numbers 0,1,2,3,4…

integers …−3,−2,−1,0,1,2,3,4…

Multiple Choice

An example of a whole number is:

4/9

-9

5.2

Multiple Select

Classify the number (choose all that apply): -20

positive number

whole number

integer

rational number

Multiple Choice

What is the best classification for this number? (how far down can you push this into the Venn Diagram)

none of these

whole

integer

rational

Multiple Choice

What is the best classification for this number? (how far down can you push this into the Venn Diagram)

-4

none of these

whole

integer

rational

Rational Numbers

A rational number is a number that can be written in the form p/q

where p

and q

are integers

and q≠o.

All fractions, both positive and negative, are rational numbers.

A few examples are:

4/5, −7/8, 13/4, and −20/3

Multiple Choice

Is 100/36 a rational number?

Yes

Multiple Choice

Is 0 a rational number?

Yes

Multiple Choice

Is ⅔ a rational number?

Yes

Multiple Choice

Is $\sqrt{7}$ a rational number?

Yes

Irrational numbers

Are there any decimals that do not stop or repeat?

The number π (the Greek letter pi, pronounced ‘pie’), which is very important in describing circles, has a decimal form that does not stop or repeat.

π=3.141592654.......

A decimal that does not stop and does not repeat cannot be written as the ratio of integers. We call this kind of number an irrational number.

Multiple Select

Identify the rational numbers. (Select all that apply)

$\sqrt{4}$

$\pi$

$3.5$

$\sqrt{2}$

$\frac{2}{3}$

Multiple Choice

Is the following number rational or irrational?

-17.5

Rational

Irrational

Multiple Choice

Is the following number rational or irrational?

√25

Rational

Irrational

Multiple Choice

Which number is a rational number?

1/4

√3

Multiple Choice

Which number is irrational?

9.6

√45

3/8

3.4 x 10 ⁵

Multiple Choice

Is -32 a rational number?

Yes

Multiple Choice

12 + 7 = 7 + 12
What property is this?

Commutative Property of Addition

Commutative Property of Multiplication

Distributive Property

Identity Property of Addition

Multiple Choice

Commutative Property of Multiplication

8 + 2 = 2 + 8

7 x 1 = 7

7 + 0 = 7

7 x 6 = 6 x 7

Multiple Choice

Name the property showed by the following statement.
(3 x 3)5 = 5(3 x 3)

Commutative Property

Associative Property

Distributive Property

Multiplication Property of One (Identity)

Multiple Choice

Which of these illustrates the Associative Property of Multiplication?

4x(5x6)=(4x5)x6

6+(9+1)=(6x9)+1)

4 x (56) = (45) x 6

5 + 0 = 0 + 5

Multiple Choice

Which is an example of Associative Property of Addition?

(12+3)+8=12x(3x8)

12x(3x8)=(12x3)x8

(12+8)+3=12+(8+3)

12 + 18 = 18 + 12

Multiple Choice

(30 + 20) + 60 = 30 + (20 + 60)

Associative Property of Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

The Properties of Real Numbers

by Dr. Luis Bello

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