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1.3 – Properties of Real Numbers

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Real Numbers 1.3 – Properties of Real Numbers

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Real Numbers (R)

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1.3 – Properties of Real Numbers Real Numbers (R)

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1.3 – Properties of Real Numbers Real Numbers (R) Rational

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1.3 – Properties of Real Numbers Real Numbers (R) Rational (⅓)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Integers

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Integers (-6)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) Whole #’s

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) Whole #’s (0)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) Natural #’s

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) Natural #’s (7)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (7)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

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1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Irrational (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

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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)

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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)

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Example 1

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Name the sets of numbers to which each apply.

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Example 1 Name the sets of numbers to which each apply.

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Example 1 Name the sets of numbers to which each apply.

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Example 1 Name the sets of numbers to which each apply. (a) √ 16

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Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4

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Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N

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Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N, W

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Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N, W, Z

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Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N, W, Z, Q

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Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N, W, Z, Q, R

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Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185

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Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z

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Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q

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Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Example 2

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Name the property used in each equation.

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Example 2 Name the property used in each equation. (a) (5 + 7) + 8 = 8 + (5 + 7)

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Example 2 Name the property used in each equation. (a) (5 + 7) + 8 = 8 + (5 + 7) Commutative Addition

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Example 2 Name the property used in each equation. (a) (5 + 7) + 8 = 8 + (5 + 7) Commutative Addition (b) 3(4x) = (3·4)x

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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

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Example 3 What is the additive and multiplicative inverse for -1¾?

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Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾

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Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + = 0

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Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + 1¾ = 0

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Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + 1¾ = 0 Multiplicative: -1¾

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Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + 1¾ = 0 Multiplicative: -1¾ · = 1

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Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + 1¾ = 0 Multiplicative: (-1¾)(- 4 / 7 ) = 1

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1.4 – The Distributive Property

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

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Example 4

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Simplify 2(5m+n)+3(2m–4n).

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n)

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n)

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n)

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m +

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n +

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m –

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n 10m + 6m + 2n – 12n

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n 10m + 6m + 2n – 12n 16m

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Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n 10m + 6m + 2n – 12n 16m – 10n

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223 Reference Chapter Section R2: Real Numbers and Their Properties Natural Numbers: {1, 2, 3, 4, …} Whole Numbers: {0, 1, 2, …} Integers: {…, -3, -2,

223 Reference Chapter Section R2: Real Numbers and Their Properties Natural Numbers: {1, 2, 3, 4, …} Whole Numbers: {0, 1, 2, …} Integers: {…, -3, -2,

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