Sets of Real Numbers and Properties of Numbers

Multiple Select

Select ALL the numbers that can be represented as a decimal.

• 5

• 6.3

• $$\frac{3}{4}$$

• -3

• -2.65

Multiple Select

Select all the sets 1/2 belongs.

• Real

• Rational

• Irrational

• Integers

• Whole

ALL the numbers on the last slide are Real Numbers. They can all be represented as a decimal.

• Whole numbers are real numbers

• Integers are real numbers

• Rational numbers are real numbers

• Irrational numbers are real numbers

What exactly is a whole number?

• Any of the numbers 0, 1, 2, 3, 4, 5, ...

• They start at 0 and continue to infinity.

Multiple Select

Select all the whole numbers.

• 0

• 4

• 5.2

• $$\frac{2}{3}$$

• -3

What are integers?

• They are whole numbers and their opposites.

• They include ... -4, -3. -2, -1, 0, 1, 2, 3, 4, ...

• You will not see fractions (they are not integers)

Multiple Select

Select all the integers.

• -3

• 5

• $$-\frac{2}{3}$$

• 0

• -1.3

What are rational numbers?

• They are whole numbers.

• They are integers.

• They now include any positive or negative number...this includes fractions.

• Remember fractions are decimals that either terminate or repeat!

Multiple Select

Select all the rational numbers.

• $$\frac{1}{2}$$

• 5.2

• 4

• 0

• $$\pi$$

What are irrational numbers?

Multiple Select

Select all the irrational numbers.

• 4

• 3.2

• $$\sqrt{6}$$

• $$\pi$$

• $$\sqrt{25}$$

Multiple Select

Select all the sets 1/2 belongs.

• Real

• Rational

• Irrational

• Integers

• Whole

Multiple Select

Select all the sets 30% belongs.

• Real

• Rational

• Irrational

• Integers

• Whole

Multiple Select

Select all the sets -16 belongs.

• Real

• Rational

• Irrational

• Integers

• Whole

Multiple Select

Select all the sets 14 belongs.

• Real

• Rational

• Irrational

• Integers

• Whole

Multiple Select

Select all the sets $$\sqrt[]{6}$$   belongs.

• Real

• Rational

• Irrational

• Integers

• Whole

Try-It

Try to Label the Venn Diagram and

complete the worksheet.

​

​Worksheet- Resource Master 71

Properties

• Additive Identity property

• Additive inverse property

• Opposite of an opposite property (Op-op property)

Properties of Numbers

Additive Identity Property

• When adding 0 to a number, the number keeps its identity.

• For any real number n, n + 0 = n

• Examples:

• 8 + 0 = 8

• 9 = 0 + 9

• -3 + 0 = -3

Multiple Select

Select all the examples that depict the Additive Identity Property of Zero.

• 9 + -9 = 0

• 8 + 0 = 8

• $$\frac{1}{2}+0=\frac{1}{2}$$

• $$-3=-3+0$$

• $$0=-5+5$$

Additive Inverse Property

Multiple Select

Select all the examples that depict the Additive Inverse Property.

• $$3+0=3$$

• $$-2.1+2.1=0$$

• $$0=\frac{2}{3}+-\frac{2}{3}$$

• $$-5=-5+0$$

Opposite of an Opposite Property

(Op-Op Property)

Multiple Select

Select which equations are true using the Op-Op Property.

• $$-\left(-7\right)=-7$$

• $$-\left(-6\right)=6$$

• $$-\left(-\left(-3\right)\right)=3$$

• $$-\left(-\left(-x\right)\right)=-x$$