The Real Number System

The Real Number System

Classifying Numbers and Their Properties

Irrational Numbers

• are decimals that never end... think Pi

• are non-perfect square roots

• ARE ALSO REAL NUMBERS

• CANNOT BE RATIONAL NUMBERS. 

Multiple Select

Check all of the IRRATIONAL numbers.

•  $4.13254981321985164...$  

•  $\sqrt{4}$  

•  $\pi$  

•  $\sqrt{73}$  

• 2.57

Rational Numbers

• can be written as a fraction (1/2)

• are decimals that have a repeating pattern (1.32323232...)

• are decimals that terminate (2.75)

• are ALL numbers that aren't irrational (like 3 or -57).

• ARE ALSO REAL NUMBERS

• CANNOT BE IRRATIONAL.

Multiple Select

Select all of the RATIONAL numbers.

• $\frac{1}{16}$

• $\pi$

• $\sqrt{36}$

• 1.333333...

• 2.51354832156...

Rational Numbers are broken down into 3 subsets:

• Integers

• Whole Numbers

• Natural Numbers

Integers

• are counting numbers on a number line. This includes negative numbers.

• do not include decimals or fractions.

• ARE ALSO RATIONAL NUMBERS AND REAL NUMBERS.

Every number on the number line is an integer. 

Multiple Choice

 $1.78$  is an integer.

• True 

• False

Multiple Choice

-123 is an integer.

• True

• False

Whole Numbers

• Include POSITIVE integers

• includes ZERO

• DO NOT include negative integers

• do not include decimals or fractions

• ARE ALSO INTEGERS, RATIONAL NUMBERS, AND REAL NUMBERS.

Whole numbers start at 0 and include every positive integer on the number line. 

Multiple Choice

45 is a whole number.

• True

• False

Multiple Choice

-2 is a whole number.

• True

• False

Multiple Choice

0 is a whole number.

• True

• False

Multiple Choice

 $\pi-\pi$  is a whole number.

• True 

• False

Natural Numbers

• include the integers on a number line STARTING AT 1.

• DO NOT include 0.

• DO NOT include negative numbers. 

• DO NOT include fractions and decimals

• ARE ALSO WHOLE NUMBERS, INTEGERS, RATIONAL NUMBERS, AND REAL NUMBERS.

Natural numbers start at 1 and include every positive integer on the number line. 

Multiple Choice

0 is a natural number.

• True

• False

Multiple Choice

56 is a natural number.

• True

• False

Multiple Choice

 $\frac{36}{4}$  is a natural number. 

• True 

• False

Multiple Select

Select ALL SETS to which

 $-\frac{5}{3}$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Multiple Select

Select ALL SETS to which

 $\sqrt{25}$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Multiple Select

Select ALL SETS to which

 $0.333333333...$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Multiple Select

Select ALL SETS to which

 $\sqrt{2}-\sqrt{2}$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Multiple Select

Select ALL SETS to which

 $\sqrt{31}$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Multiple Select

Select ALL SETS to which

 $2\ \frac{5}{7}$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Multiple Select

Select ALL SETS to which

 $-0.78$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Multiple Select

Select ALL SETS to which

 $\sqrt{\frac{4}{16}}$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Multiple Select

Select ALL SETS to which

 $\frac{35}{7}$  belongs. It is also REAL.

• Irrational

• Rational

• Integer

• Whole Number

• Natural Number

Commutative Property

• order of values does not matter

• 7+8=8+7

• (9*4)+6=6+(9*4)

• 5*4=4*5

Multiple Choice

Which equation represents the Commutative Property?

• $5+0=5$

• $3\left(x+1\right)=3x+3$

• $2+\left(7\cdot4\right)=\left(7\cdot4\right)+2$

Associative Property

• The grouping of values does not matter! Move parentheses.

• (a+b)+c=a+(b+c)
  

• (5+1)+3=5+(1+3)

Multiple Choice

Which equation represents the associative property?

• $\left(5x+2y\right)+6=5x+\left(2y+6\right)$

• $2+0=2$

• $7+\left(-7\right)=0$

Identity Property

• Stays the same!!

• a+0=a

• b*1=b

• 4(1)=4

• 3+0=3

Multiple Choice

Which equation represents the identity property?

• $17\cdot0=0$

• $2+3=3+2$

• $5\cdot\frac{1}{5}=1$

• $4+0=4$

Inverse Property

• uses the opposite to "cancel" a value!

• a+(-a)=0

• 3*(1/3)=1

Multiple Choice

Which equation represents the inverse property?

• $\left(2\cdot4\right)\cdot7=2\cdot\left(4\cdot7\right)$

• $5\cdot1=5$

• $7\cdot\frac{1}{7}=1$

• $2\left(4x+3\right)=8x+6$

Distributive Property

• Multiply a value to an expression inside parentheses. 

• a(b+c)=ab+ac

• 2(x+6)=2x+12

Multiple Choice

Which equation represents the Distributive Property?

• $3+\left(6\cdot4\right)=\left(6\cdot4\right)+3$

• $x\left(2y+7\right)=2xy+7x$

• $xy=yx$

Poll

After this lesson, I feel confident on classifying numbers.

• I'm ready for the quiz!

• I feel okay about it.

• I could use a little more help.

• I'm completely lost still.

Poll

After this lesson, I feel confident on naming the number properties.

• I'm ready for the quiz!

• I feel okay about it.

• I could use a little more help.

• I'm completely lost still.