1.3 – Properties of Real Numbers. Real Numbers 1.3 – Properties of Real Numbers

1.3 – Properties of Real Numbers

Real Numbers

1.3 – Properties of Real Numbers

1.3 – Properties of Real Numbers

Real Numbers (R)

1.3 – Properties of Real Numbers

Real Numbers (R)

1.3 – Properties of Real Numbers

Real Numbers (R)

Rational

1.3 – Properties of Real Numbers

Real Numbers (R)

Rational (⅓)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

Integers

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

Integers (-6)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

Whole #’s

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

Whole #’s (0)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

Natural #’s

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

Natural #’s (7)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (7)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (1)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓) Irrational

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (1)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓) Irrational √ 5

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (1)

1.3 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓) (I) Irrational √ 5

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (1)

Example 1

Example 1

Name the sets of numbers to which each apply.

Example 1

Name the sets of numbers to which each apply.

Example 1

Name the sets of numbers to which each apply.

Example 1

Name the sets of numbers to which each apply.

(a) √ 16

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q, R

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q, R

__

(e) 0.45

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q, R

__

(e) 0.45 - Q

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q, R

__

(e) 0.45 - Q, R

Properties of Real Numbers

Property Addition Multiplication

Commutative a + b = b + a a·b = b·a

Associative (a+b)+c = a+(b+c) (a·b)·c = a·(b·c)

Identity a+0 = a = 0+a a·1 = a = 1·a

Inverse a+(-a) =0= -a+a a·1 =1= 1·a

a a

Distributive a(b+c)=ab+ac and (b+c)a=ba+ca

Example 2

Example 2

Name the property used in each equation.

Example 2

Name the property used in each equation.

(a) (5 + 7) + 8 = 8 + (5 + 7)

Example 2

Name the property used in each equation.

(a) (5 + 7) + 8 = 8 + (5 + 7)

Commutative Addition

Example 2

Name the property used in each equation.

(a) (5 + 7) + 8 = 8 + (5 + 7)

Commutative Addition

(b) 3(4x) = (3·4)x

Example 2

Name the property used in each equation.

(a) (5 + 7) + 8 = 8 + (5 + 7)

Commutative Addition

(b) 3(4x) = (3·4)x

Associative Multiplication

Example 3

What is the additive and multiplicative inverse for -1¾?

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + = 0

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + 1¾ = 0

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + 1¾ = 0

Multiplicative: -1¾

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + 1¾ = 0

Multiplicative: -1¾ · = 1

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + 1¾ = 0

Multiplicative: (-1¾)(-4/7) = 1