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Associative Property of Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

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

(a x b) x c = a x (b x c)

a + b = b + a

a x b = b x a

Associative Property of Addition

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

Associative Property of Multiplication

(a x b) x c = a x (b x c)

1. Associative Property of Addition

2. Associative Property of Multiplicat…

3. Commutative Property of Addition

4. Commutative Property of Multiplicat…

When three or more numbers are added, the sum is the same reg…

When three or more numbers are multiplied, the product is the…

When two or more numbers are added, the sum is the same regar…

When two numbers are multiplied together, the product is the…

1. Associative Property of Addition

When three or more numbers are added, the sum is the same reg…

2. Associative Property of Multiplicat…

When three or more numbers are multiplied, the product is the…

Associative Property of Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

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

(a x b) x c= a x (b x c)

a + b = b + a

a x b = b x a

Associative Property of Addition

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

Associative Property of Multiplication

(a x b) x c= a x (b x c)

1. Associative Property of Addition

2. Associative Property of Multiplicat…

3. Commutative Property of Addition

4. Commutative Property of Multiplicat…

When three or more numbers are added, the sum is the same reg…

When three or more numbers are multiplied, the product is the…

When two or more numbers are added, the sum is the same regar…

When two numbers are multiplied together, the product is the…

1. Associative Property of Addition

When three or more numbers are added, the sum is the same reg…

2. Associative Property of Multiplicat…

When three or more numbers are multiplied, the product is the…

Additive Identity

Multiplicative Identity

Multiplicative Property Of Zero

Commutative Property of Addition

When 0 is added to any number, the sum is the number.

Any number multiplied by 1, product is the number.

When any number is multiplied by 0, product is 0.

The order in which numbers are added does not change the sum.

Additive Identity

When 0 is added to any number, the sum is the number.

Multiplicative Identity

Any number multiplied by 1, product is the number.

Identity property of multiplication

Commutative property of multiplication

Inverse property of multiplication

Reflexive

The product of any number and one is that number ... a x 1 =a

When two numbers are multiplied together, the product is the…

The multiplicative inverse of a number , a is 1/a so that a x…

The equals sign is like mirror, and the image it "reflects" i…

Identity property of multiplication

The product of any number and one is that number ... a x 1 =a

Commutative property of multiplication

When two numbers are multiplied together, the product is the…

Piece-wise linear functions

Quadratic Function

Exponential function

Commutative Property of Addition

A function composed of linear segments to form a graph.

A function that always results in a U-shaped curve called a p…

A function whose value is a constant of the argument

The order of the numbers doesn't matter in addition

Piece-wise linear functions

A function composed of linear segments to form a graph.

Quadratic Function

A function that always results in a U-shaped curve called a p…

Substitution Property of Equality

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

If two quantities are equal, then one quantity can be replace…

The order in which numbers are added does not change the sum.

The order in which numbers are multiplied does not change the…

The way in which numbers are grouped when added does not chan…

Substitution Property of Equality

If two quantities are equal, then one quantity can be replace…

Commutative Property of Addition

The order in which numbers are added does not change the sum.

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Additon

Associative Property of Multiplication

(move; change order)... 2 + 3 + 4 = 4 + 2 +3

(changing order)... 9 x 8 x 7 = 8 x 7 x 9

(changing grouping, move the parenthesis)... 5 + (10 + 15) = 10…

(changing grouping)... 2 (5 x 7) = 7 (2 x 5)

Commutative Property of Addition

(move; change order)... 2 + 3 + 4 = 4 + 2 +3

Commutative Property of Multiplication

(changing order)... 9 x 8 x 7 = 8 x 7 x 9

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Additon

Associative Property of Multiplication

(move; change order)... 2 + 3 + 4 = 4 + 2 +3

(changing order)... 9 x 8 x 7 = 8 x 7 x 9

(changing grouping, move the parenthesis)... 5 + (10 + 15) = 10…

(changing grouping)... 2 (5 x 7) = 7 (2 x 5)

Commutative Property of Addition

(move; change order)... 2 + 3 + 4 = 4 + 2 +3

Commutative Property of Multiplication

(changing order)... 9 x 8 x 7 = 8 x 7 x 9

Commutative Property

Associative Property

Additive Inverse

Additive Identity

abs=b+a a**b=b**a ... (doesn't work on division nor subtraction s…

(a+b)+c=a+(b+c) (ab)c=a(bc)... (doesn't work on division nor su…

a+(-a)=0

a+0=a

Commutative Property

abs=b+a a**b=b**a ... (doesn't work on division nor subtraction s…

Associative Property

(a+b)+c=a+(b+c) (ab)c=a(bc)... (doesn't work on division nor su…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b + c = b + a + c

a x b = b x a

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

(a x b) x c = a x (b x c)

Commutative Property of Addition

a + b + c = b + a + c

Commutative Property of Multiplication

a x b = b x a

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

States that changing the order in which the numbers are added…

States that changing the order in which numbers are multiplie…

States that changing the grouping of addends does not change…

States that changing the grouping of factors does not change…

Commutative Property of Addition

States that changing the order in which the numbers are added…

Commutative Property of Multiplication

States that changing the order in which numbers are multiplie…

Associative Property

Communicative Property

Distributive Property

Additive Identity Property

Changing the grouping of numbers will NOT change the value. F…

The order in which addition or multiplication is done does no…

a(b + c) = ab + ac;... a property indicating a special way in wh…

a + 0 = a

Associative Property

Changing the grouping of numbers will NOT change the value. F…

Communicative Property

The order in which addition or multiplication is done does no…

Commutative Property

Associative Property

Identity Property of Addition

Identity Property of Multiplication

Changing the order of the numbers in the expression does not…

Changing the grouping of the numbers in the expression does n…

Adding 0 to a number does not change the value of the number…

Multiplying a number by 1 does not change the value of the nu…

Commutative Property

Changing the order of the numbers in the expression does not…

Associative Property

Changing the grouping of the numbers in the expression does n…

Identity Property of Addition

Identity Property of Multiplication

Multiplicative Property of Zero

Commutative Property of Addition

Algebriac: a+ 0= a 3 + 0=3... I can add zero to anything withou…

Algebriac: a x 1=a 3 x 1=3... I can multiply anything by 1 and…

Algebreic: a x 0= 0 3 x 0=0... Anything times zero is zero.

Algebriac: a+b is the same as b+a ... This means that you can a…

Identity Property of Addition

Algebriac: a+ 0= a 3 + 0=3... I can add zero to anything withou…

Identity Property of Multiplication

Algebriac: a x 1=a 3 x 1=3... I can multiply anything by 1 and…

The Distributive Property

Example 2.1.1

Example 2.1.2

Example 2.1.3

The distributive property of mathematics states that when a s…

5(3 + 2)... = (5 x 3) + (5 x 2)... = 15 + 10... = 25

4 (2 + 3 - 1) =... (4 x 2) + (4 x 3) - (4 x 1)... = 8 + 12 - 4... = 16

6 (4 - 2 + 3 - 1)... = (6 x 4) - (6 x 2) + (6 x 3) - (6 x 1)... = 2…

The Distributive Property

The distributive property of mathematics states that when a s…

Example 2.1.1

5(3 + 2)... = (5 x 3) + (5 x 2)... = 15 + 10... = 25

zero property of x

commutative property of addition or mu…

identity property of addition

identity property of multiplication

X x 0 =0... any number multiplied by 0 equals 0

a+b=b+a... Changing the order of the addends does not change the…

The sum of any number and 0(zero) is equal to the initial num…

The product of any number and 1 is equal to the original numb…

zero property of x

X x 0 =0... any number multiplied by 0 equals 0

commutative property of addition or mu…

a+b=b+a... Changing the order of the addends does not change the…

Identity Laws

Reflexive Property

Symmetric Property

Transitive Property

a + 0 = a... a - 0 = a ; a - a = 0... a * 1 = a... a ÷ 1 = a ; a ÷ a = 1

a = a

If a = b, then b = a

If a = b and b = c, then a = c

Identity Laws

a + 0 = a... a - 0 = a ; a - a = 0... a * 1 = a... a ÷ 1 = a ; a ÷ a = 1

Reflexive Property

a = a

algebraic expression

binomial

cancel

coefficient

a group of terms that are joined by addition or subtraction s…

an algebraic expression consisting of two terms

to simplify a fraction by dividing the numerator and denomina…

the number that multiplies a pronumeral in an algebraic expre…

algebraic expression

a group of terms that are joined by addition or subtraction s…

binomial

an algebraic expression consisting of two terms

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Add numbers in any order equals the same sum... ***CoMOVEative..…

Multiplying numbers in any order equals the same product... ***C…

Grouping the numbers differently doesn't change the sum... ***pa…

Grouping the numbers differently doesn't change the product... *…

Commutative Property of Addition

Add numbers in any order equals the same sum... ***CoMOVEative..…

Commutative Property of Multiplication

Multiplying numbers in any order equals the same product... ***C…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Additon

Associative Property of Multiplication

(move; change order)... 2 + 3 + 4 = 4 + 2 +3

(changing order)... 9 x 8 x 7 = 8 x 7 x 9

(changing grouping, move the parenthesis)... 5 + (10 + 15) = 10…

(changing grouping)... 2 (5 x 7) = 7 (2 x 5)

Commutative Property of Addition

(move; change order)... 2 + 3 + 4 = 4 + 2 +3

Commutative Property of Multiplication

(changing order)... 9 x 8 x 7 = 8 x 7 x 9

Factors

Multiple

Divisibility Rule

GCF

Numbers multiplied to equal a larger number

Number composed of two or more factors

A way of identifying the factors of a multiple

The greatest common factor of two or more multiples

Factors

Numbers multiplied to equal a larger number

Multiple

Number composed of two or more factors

Substitution Property

Additive Identity Property

Multiplicative Identity Property

Additive Inverse Property

If a=b, then "a" may be replaced by "b" in an expresion.

a+0=a

a•1=a

a+(-a)=0

Substitution Property

If a=b, then "a" may be replaced by "b" in an expresion.

Additive Identity Property

a+0=a

Associative Property of Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

This property states that when adding, the grouping doesn't m…

This property states that when multiplying, the grouping does…

This property states that when adding, the order doesn't matt…

This property states that when multiplying, the order doesn't…

Associative Property of Addition

This property states that when adding, the grouping doesn't m…

Associative Property of Multiplication

This property states that when multiplying, the grouping does…

Additive Identitiy

Multiplacative Identity

Additive Inverse

Multiplicative Inverse

Any number + 0 = the same number

Any number times 1 = the same number

Any number + it's opposite = 0

Any number times it's reciprocal = 1

Additive Identitiy

Any number + 0 = the same number

Multiplacative Identity

Any number times 1 = the same number

Additive Identity Property

Multiplicative Identity Property

Additive Inverse Property

Multiplicative Inverse Property

Any number plus zero equals the same number as zero

Any number times one equals the same number

Any number plus it's opposite equals zero

Any number times its reciprocal equals one

Additive Identity Property

Any number plus zero equals the same number as zero

Multiplicative Identity Property

Any number times one equals the same number

commutative property

associative property

addition property of zero

multiplication property of zero

changing the order of addends or factors does not change the…

changing the grouping of addends or factors does not change t…

the sum of any number and ) is that number ... 18 + 0= 18 or w +…

the product of any number and 0 is 0 ... 9 x 0 = 0 a x 0 = 0

commutative property

changing the order of addends or factors does not change the…

associative property

changing the grouping of addends or factors does not change t…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b + c = b + a + c

a x b = b x a

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

(a x b) x c = a x (b x c)

Commutative Property of Addition

a + b + c = b + a + c

Commutative Property of Multiplication

a x b = b x a

(3 + 4) + 5 = 3 + (4 + 5)

4 + (-4) = 0

7 x (8 x 1) = (7 x 8) x 1

5(2 + 3a) = (5 x 2) + (5 x 3a)

Associative property of addition

Additive Inverse

Associative property of multiplication

Distributive property

(3 + 4) + 5 = 3 + (4 + 5)

Associative property of addition

4 + (-4) = 0

Additive Inverse

Commutative Property of Addition

Commutative Property of Multiplication

Identity Property of Addition

Identity Property of Multiplication

Changing the order of the addends does not change the sum.

Changing the order of the factors does not change the produce

If you add zero to a number, the sum is the same as that numb…

If you multiply a number by one, the product is the same as t…

Commutative Property of Addition

Changing the order of the addends does not change the sum.

Commutative Property of Multiplication

Changing the order of the factors does not change the produce

Additive Identity

Additive Inverse

Associative Property of Addition

Commutative Property of Addition

Any number added to zero is the number you started with.... Ex.…

The opposite of the number you started with will equal 0.... Ex.…

Changing the groupings... Ex. 5 + (2 + 8) = (5 + 2 ) + 8

Changing the order of the numbers.... Ex. 8 + 9 + 3 = 3 + 9 + 8

Additive Identity

Any number added to zero is the number you started with.... Ex.…

Additive Inverse

The opposite of the number you started with will equal 0.... Ex.…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b + c = b + a + c

a x b = b x a

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

(a x b) x c = a x (b x c)

Commutative Property of Addition

a + b + c = b + a + c

Commutative Property of Multiplication

a x b = b x a

Additive Identity

Commutative Property of Addition:

Associative Property of Addition:

Multiplicative Identity:

a + 0 = a... 3 + 0 = 3... 6 + 0 = 6

a + b = b + a... 3 + 6 = 6 + 3... 7 + 2 = 2 + 7

(a + b) + c = a + (b + c)... (3 + 4) + 6 = 3 + (4 + 6)... (5 + 3) +…

a ● 1 = a... 3 ● 1 = 3... 6 ● 1 = 6

Additive Identity

a + 0 = a... 3 + 0 = 3... 6 + 0 = 6

Commutative Property of Addition:

a + b = b + a... 3 + 6 = 6 + 3... 7 + 2 = 2 + 7

Additive Identitiy

Additive Inverse ( opposites)

Multiplicative Identity

Multiplicative property of zero

zero is added because you can add it to a number without chan…

3 and -3 because 3+-3=0. equal zeo

multiply by one because you can multiply it by a number and t…

multiply any number by 0 and you get 0

Additive Identitiy

zero is added because you can add it to a number without chan…

Additive Inverse ( opposites)

3 and -3 because 3+-3=0. equal zeo

Communicative property

Associated property

Addeitive property

Multiplicative identity

Is the order in which they are added or multipled does not ch…

States that the way in which numbers are grouped when added o…

When 0 is added to any number ,the sum in the number

When any number is multiplied by 1 ,The product is the number

Communicative property

Is the order in which they are added or multipled does not ch…

Associated property

States that the way in which numbers are grouped when added o…

Identity Property of Addition

Zero Property of Multiplication

Commutative Property of Addition

Associative Property of Addition

Adding 0 does not change the value of a number.... Examples: 7 +…

Multiplying by 0 results in a product of 0.... Examples: 8 x 0 =…

Changing the order of the addends does not change the sum.... Ex…

Changing the grouping of addends does not change the sum.... Exa…

Identity Property of Addition

Adding 0 does not change the value of a number.... Examples: 7 +…

Zero Property of Multiplication

Multiplying by 0 results in a product of 0.... Examples: 8 x 0 =…

Commutative property of multiplication

Commutative property of addition

Associative property of multiplication

Identity property of multiplication

3 × 4 = 4 × 3

8 + 2 = 2 + 8

( 6 × 2 ) × 5 = 6 × ( 2 × 5 )

n × 1 = n

Commutative property of multiplication

3 × 4 = 4 × 3

Commutative property of addition

8 + 2 = 2 + 8

8 + 9 = 9 + 8

0 + 7 = 7 + 0

6 x (-2) = (-2) x 6

4 x 1 = 1 x 4

Commutative Property of Addition

Commutative Property of Addition

Commutative Property of Multiplication

Commutative Property of Multiplication

8 + 9 = 9 + 8

Commutative Property of Addition

0 + 7 = 7 + 0

Commutative Property of Addition

Substitution Property

Additive Identity property

Multiplicative Identity Property

Additive Inverse Property

If a=b, then "a" may be replaced by "b" in any expression.

A+0=A

A*1= A... 1*A=A

A+(-A)= 0

Substitution Property

If a=b, then "a" may be replaced by "b" in any expression.

Additive Identity property

A+0=A