Place Value

In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right.

A number in standard form is separated into groups of three digits using commas. Each of these groups is called a period.

When a number is written in this form, it is said to be in "standard form."

The Place Value
Ten thousands	Thousands	Hundreds	Tens	Ones

Examples:

1.         35,689
        30,000 + 5,000 + 600 + 80 + 9

Thirty-five thousand, six hundred, eighty-nine

3 = Ten thousands

5 = Thousands

6 = Hundreds

8 = Tens

9 = Ones

2.         691

600 + 90 + 1

Six hundred, ninety-one

6 = Hundreds

9 = Tens

1 = Ones

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Multiplying and Dividing

•  When we multiply two integers with the same signs, the result is always positive. Just multiply the absolute values and make the answer positive.
•  When we multiply two integers with different signs, the result is always negative. Just multiply the absolute values and make the answer negative.
• When we divide two integers with the same sign, the result is always positive. Just divide the absolute values and make the answer positive.
• When we divide two integers with different signs, the result is always negative. Just divide the

Properties of Integers

1.        Commutative property of addition
The commutative property of addition says that we can add numbers in any order.

2.        Associative property of addition
The associative property of addition tells us that we can group numbers in a sum in any way we want and still get the same answer.

3.        Commutative property of multiplication
The commutative property of multiplication is very similar. It says that we can multiply numbers in any order we want without changing the result.

4.        Associative property of multiplication
The associative property of multiplication tells us that we can group numbers in a product in any way we want and still get the same answer.

5.        Distributive property
The distributive property comes into play when an expression involving addition is then multiplied by something. It tells us that we can add first and then multiply, or multiply first and then add. Either way, the multiplication is "distributed" over all the terms inside the parentheses.

6.        Subtraction is neither commutative nor associative.

7.        Division is neither commutative nor associative.

Formula

Commutative property of addition	a + b = b + a
Associative property of addition	(a + b) + c = a + (b + c)
Commutative property of multiplication	a x b = b x a
Associative property of multiplication	(a x b) x c = a x (b x c)
Distributive property	a x (b + c) = (a x b) + (a x c)

Watch Out!!!

a - b  ≠ b - a

(a - b) - c  ≠ b - (a - c)

a ÷ b  ≠ b ÷ a

(a ÷ b) ÷ c  ≠ b ÷ (a ÷ c)

Examples:

1.    Commutative property of addition

51 + 42 = 42 + 51 = 93

2.    Associative property of addition

(33 + 23) + 21 = 33 + (23 + 21) = 77

3.    Commutative property of multiplication

15 x 24 = 24 x 15 = 360

4.    Associative property of multiplication

(11 x 12) x 9 = 11 x (12 x 9) = 1188

5.    Distributive property

7 x (3 + 5) = (7 x 3) + (7 x 5) = 56