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**Chapter 1 Learning Target: 10**

Properties of Numbers Chapter 1 Learning Target: 10

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**The Commutative Property of Addition**

This property allows us to “switch” the order of how we add numbers, and still get the same answer. For example: 3+5=8 and 5+3=8 Therefore: = 5+3 In General: a+b = b+a Hint on how to remember: If I commute to work, I “move” to work, so in the commutative property => the numbers commute, or move.

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**The Commutative Property of Multiplication**

This property allows us to “switch” the order of how we multiply numbers, and still get the same answer. For example: 3(5)=15 and 5(3)=15 Therefore: 3(5) = 5(3) In General: ab = ba Hint on how to remember: If I commute to work, I “move” to work, so in the commutative property => the numbers commute, or move.

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**The Associative Property of Addition**

This property allows us to add three numbers by grouping them differently. For Example: (2 + 3) + 4 = 2 + (3 + 4) 5 + 4 = 2 + 7 9 = 9 In General: a+(b+c)=(a+b)+c Hint on how to remember: We are “associating” two different pairs of numbers.

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**The Associative Property of Multiplication**

This property allows us to multiply three numbers by grouping them differently. For Example: In General: a(bc)=(ab)c Hint on how to remember: We are “associating” two different pairs of numbers.

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**The Identity Property of Addition**

This property allows us to add zero to any number and the result is the original number. For Example: = - 5 In General: a + 0 = a Hint on how to remember: The number stays “identical” when we add zero.

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**The Identity Property of Multiplication**

This property allows us to multiply any number by one, and the result is the original number. For Example: In General: Hint on how to remember: The number stays “identical” when we multiply by 1.

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The Additive Inverse The additive inverse of a number is the opposite of that number. For example, the additive inverse of 3 is -3. In general, the additive inverse of a is –a, and the additive inverse of –a is a.

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**The Multiplicative Inverse**

The multiplicative inverse of a number is the reciprocal of that number. For example, the multiplicative inverse of 3 is In general, the multiplicative inverse of a is

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**The Inverse Property of Addition**

This property states that when we add a number and that numbers’ inverse, the result is zero. For Example: = 0 Note: The inverse of -5 is 5 In General: -a + a = 0 Hint on how to remember: You are adding a number and its inverse.

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**The Inverse Property of Multiplication**

This property states that when we multiply a number and that numbers’ inverse, the result is one. For Example: Note: The inverse of 5 is In General: Hint on how to remember: You are multiplying a number and its inverse.

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**The Distributive Property**

This property states that when we multiply a quantity by a number, we must multiply the entire quantity by that number. For Example: In General: Hint on how to remember: You are “distributing” a number to all the terms in the parenthesis – or quantity.

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The Absolute Value The absolute value of a number is the distance a number is from zero. For example: The absolute value of -5 is 5, because -5 is a distance of 5 units from 0. In general:

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**Integers Integers are whole numbers, but including negative numbers.**

Examples: Decimal numbers and fractions are not integers

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Rational Numbers Rational numbers are numbers that can be written as a fraction (ratio). Examples: Repeating decimal numbers, fractions, integers, are all rational numbers.

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