Chapter 1 Learning Target: 10 Properties of Numbers Chapter 1 Learning Target: 10

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: 3+5 = 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.

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.

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.

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.

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 + 0 = - 5 In General: a + 0 = a Hint on how to remember: The number stays “identical” when we add zero.

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.

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.

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

The Inverse Property of Addition This property states that when we add a number and that numbers’ inverse, the result is zero. For Example: - 5 + 5 = 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.

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.

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.

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:

Integers Integers are whole numbers, but including negative numbers. Examples: Decimal numbers and fractions are not integers

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