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**Operations With Real Numbers SOL 7**

Operations With Real Numbers SOL 7.3 by Lisa Beebe Chincoteague Combined School Commutative Property Associative Property Distributive Property Identity Properties Inverse Properties Multiplicative Property of Zero

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**Commutative Property (ORDER)**

The order in which numbers are added or multiplied does not change the answer. Examples: 3 + 5 = 5 + 3 Both sides equal 8. 2 · 7 = 7 · 2 Both sides equal 14.

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Commutative Property

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**Associative Property (GROUPING)**

The way in which three numbers are grouped with parentheses in addition or multiplication does not change the answer Examples: (1 + 2) + 3 = 1 + (2 + 3) Both sides equal 6. (2 · 3) · 5 = 2 · (3 · 5) Both sides equal 30.

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Associative Property

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**Distributive Property (Distribute)**

States that the product of a number and the sum (or differences) of two other numbers equals the sum (or difference) of the products of the number and each other number For any three numbers a, b, and c – it is true that a(b + c) = ab + ac

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**Distributive Property**

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**Identity Property of Addition**

A number plus zero is always itself. Example: = 11

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**Identity Property of Multiplication**

A number multiplied by 1 is always itself Example: 17 · 1 = 17

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**Additive Inverse Property**

States that the sum of a number and its additive inverse always equals zero. What you need to add to a number to get the identity Example: = 0

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**Multiplicative Inverse Property**

States that the product of a number and its multiplicative inverse (or reciprocal) always equals one What you need to multiply to a number to get the identity Example: 4 × ¼ = 1

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**Multiplicative Property of Zero**

States that the product of any real number and zero is always zero. Example: 5 × 0 = 0

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**Identify the following property: a + b = b + a**

Commutative Property of Multiplicaton Associative Property Commutative Property of addition Additive Identity Property 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Which property is shown in the equation 26 + 0 = 26?**

Inverse property of addition Inverse property of multiplication Identity property of addition Multiplicative property of zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Identity the following property: 5 · (x · y) = (5 · x) · y**

Distributive Property Associative property of multiplication Associative Property of addition Commutative property of multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Identify the following property: 5 · (x · y) = 5 · (y · x)**

Associative Property of Multiplication Associative Property of Addition Distributive Property Commutative Property of multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Which equation uses the distributive property?**

-3(4 + 7) = -3(4) + -3(7) -3(4 + 7) = -3(11) -3(4 + 7) = -3(4) + 7 -3(4 + 7) = 4(-3) + 4(7) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Which equation shows the multiplicative property of zero?**

-35.9(1) = -35.9 -35.9(0) = 0 -35.9(359/10) = 1 -35.9(35.9) = 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Which property is shown in the equation 7 × 0 = 0?**

Additive identity property Multiplicative Identity property Multiplicative inverse property Multiplicative property of zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**What is the identity for addition?**

-1 1 1/0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**What is the identity for multiplication?**

-1 1 1/0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Which of the following is the additive inverse of 4?**

-4 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Identify the property used. (1 + 3) × (4 + 1) = (1 + 3) × (1 + 4)**

Associative property of multiplication Associative property of addition Commutative property of multiplication Commutative property of addition 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**Jessica has found that ¼ × 4/1 = 1**

Jessica has found that ¼ × 4/1 = 1. She has discovered an example of _____________. the multiplicative identity the additive identity a multiplicative inverse an additive inverse 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**What is the reciprocal, or multiplicative inverse , of -3?**

1/3 -1/3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**The expression x + (-x) = 0 demonstrates which property?**

Multiplicative inverse Distributive property Additive inverse Multiplicative property of zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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**If the distributive property is applied to 5(7 + 3), which is the result?**

5(7)(3) 5(7) + 3 5(7) + 5(3) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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When adding two numbers, the order does not matter. EXAMPLES: 5 + 6 = 6 + 5 a + b = b + a.

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