Math 6 Honors Periods 1, 6 & 7

Inverse Operations 1-3


Inverse operations: mathematical operations that undo each other.
Using the same number, the operation of subtraction undoes the operation of addition
Similarly, the operation of division and multiplication can be described as inverse operations

The addition and multiplication properties of 0 and 1 lead us to the subtraction and division properties of 0 and 1

Subtraction Property of Zero

For any whole number a,
a – 0 = a and a - a = 0


Division Property of One

For any whole number a, except 0,
a ÷ 1 = a and a ÷ a = 1


Division Property of Zero

For any whole number a, except 0,
0 ÷ a = 0

Notice in the division property of 0 that the divisor, a, represents any whole number, except for 0.

Math 6 H Periods 1, 6 & 7 (Tues & Wed.)

Mathematical Expressions 1-1

A variable is a symbol used to represent one or more numbers. The numbers are called the values of the variable.

An expression, such as 3 x n, that involves a variable is called a variable expression.

Expressions, such as 3 x 2, that name a certain number are called numerical expressions

When we write a product that involves a variable, we usually omit the multiplication symbol (whether that be written as x or as ∙ or even with parentheses). Thus, 3 x n is written as 3n

and 2 x a x b is written as 2ab

In numerical expressions for products a multiplication symbol must be used to avoid confusion.

9 x 7 may be written as 9 ∙ 7

When a mathematical sentence uses an equal sign, it is called an equation. An equation tells us that two expressions name the same number. The expression to the left of the equals sign is called the left side of the equation and the expression to the right of the equals sign is called the right side.

When a number is substituted for a variable in the variable expression and the indicated operation is carried out, we say that the variable expression has been evaluated. For example, if n has the value 6 in the variable expression 3 x n, then 3 x n has the value 3 x 6, or 18

Properties of Addition and Multiplication 1-2

The set of numbers 1, 2, 3, 4, 5, … is called the counting numbers.

If 0 is included in the set, we obtain the set of whole numbers

0, 1, 2, 3, 4, …

The order in which two whole numbers are added or multiplied does not change their sum or their product.

For example, 3 + 4 = 7 and 4 + 3 = 7

3 x 4 = 12 and 4 x 3 = 12

Commutative Properties

For any whole numbers a and b, a + b = b + a

For any whole numbers a and b, a x b = b x a

C+ for Commutative Property of addition

Cx for Commutative Property of multiplication

Operations indicated within parentheses in any expression are done before the others.

(9 x 2) x 5 = 18 x 5 = 90

9 x (2 x 5) = 9 x 10 = 90

The order in which we multiply whole numbers has no effect on the product

(9 x 2) x 5 = 9 x (2 x 5)

Associative Properties

For any whole numbers a, b, and c,

(a + b) + c = a + (b + c)

For any whole numbers a, b, and c, (a x b) x c = a x (b x c)

A+ for Associative Property of Addition

Ax for Associative Property of Multiplication

The numbers 0 and 1 have special properties.

6 + 0 = 6 and 0 + 6 = 6

Since the sum of any whole number and 0 is the same whole number, 0 is called the identity element for addition

Addition Property of Zero

For any whole number a,

a + 0 = a and 0 + a = a

It’s the Identity Property of Addition also know as the Additive Identity

Id+

6 x 1 = 6 and 1 x 6 = 6

1 is the identity element for multiplication, since the product of any whole number and 1 is the same whole number.

Multiplication Property of One

For any whole number a,

a x 1 = a and 1 x a = a

It’s the Identity Property of Multiplication also know as the

Multiplicative Identity

Idx

6 x 0 = 0 and 0 x 6 = 0

illustrate an important property of 0—the product of any whole number and 0 is 0

Multiplication Property of Zero

For any whole number a,

a x 0 = 0 and 0 x a = 0

x0 ( my abbreviation for the multiplication property of Zero)

Pre Algebra Period 2 (Tuesday)

The Order Of Operations 1-2

O³ = Order Of Operations

It’s Aunt Sally’s Rule—Please Excuse My Dear Aunt Sally

Please (XX)

Excuse E²

My Dear (or even Dear My) × ÷ or ÷ ×

Aunt Sally (Sally Aunt) + - or - +

PEMDAS

The most common mistake of O³

when you see multiplication and division—you do whichever comes first in order!!

So if you see division then multiplication, you do division first then multiplication

When you see addition and subtraction, you do whichever comes first in order!
So if you see subtraction then addition, do the subtraction first!

When you see more than one set of parentheses, do the innermost ones first, then work outwards.
They're called nested parentheses because a bird builds his nest from the inside out.

Algebra Period 3 (Tuesday)

Symbols and Expressions 1-1

O³ = Order Of Operations

It’s Aunt Sally’s Rule—Please Excuse My Dear Aunt Sally

Please (XX)

Excuse E²

My Dear (or even Dear My) × ÷ or ÷ ×

Aunt Sally (Sally Aunt) + - or - +

PEMDAS

The most common mistake of O³

when you see multiplication and division—you do whichever comes first in order!!

So if you see division then multiplication, you do division first then multiplication

When you see addition and subtraction, you do whichever comes first in order!
So if you see subtraction then addition, do the subtraction first!

When you see more than one set of parentheses, do the innermost ones first, then work outwards.
They're called nested parentheses because a bird builds his nest from the inside out.