1.3 – Properties of Real Numbers
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
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) Z
Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b) Z, Q
Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b) Z, Q, R
Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b) 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) 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) 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) 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) 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) 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) Z, Q, R (c)√ 20 - I, R (d) -⅞ - Q, R __ (e) Q
Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b) Z, Q, R (c)√ 20 - I, R (d) -⅞ - Q, R __ (e) Q, R
Properties of Real Numbers PropertyAdditionMultiplication Commutativea + b = b + aa·b = b·a Associative (a+b)+c = a+(b+c) (a · b) · c = a · (b · c) Identitya+0 = a = 0+aa·1 = a = 1·a Inversea+(-a) =0= -a+aa·1 =1= 1·a a a Distributivea(b+c)=ab+ac and (b+c)a=ba+ca
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