Numerical Expression: 2* 1/2=1

Algebraic Expression: a*1/a=1

Shortcut: States that every non-zero number "a", when multiplied by "1/a",

gives the 1 as the answer.

**Algebraic Properties**

**By: Melissa Ignacio & GeAnn Santos**

Block: 2

Block: 2

Inverse Property of Addition

Numerical Expression: 1-1=0 or -1+1=0

Algebraic Expression: a-a=0 or -a+a=0

Shortcut: If you add a number and it's negative number together, or subtract a number from an identical one, this property is being implied.

Distributive Property

Numerical Expression: 1(2+3)= 1(2)+1(3)

Algebraic Expression: a(b+c)= a(b)+a(c)

Shortcut: A property that indicates a special way in which multiplication is applied to addition with two or more numbers.

Numerical Expression: 2*1=2

Algebraic Expression: a*1=a

Shortcut: States that the product of 1 and any number or variable is the number or variable itself.

Identity Property of Multiplication

Property of Zero

Numerical Expression: 1+0=1

Algebraic Expression: a*0=0

Shortcut: The sum of any number and zero is that number. The product of any number and zero is zero.

Associative Property of Addition

Numerical Expression: (1+2)+3= 1 +(2+3)

Algebraic Expression: (a+b)+c= a+(b+c)

Shortcut: When two or more numbers are added, the sum is the same regardless of the order of addition.

**The algebraic properties in mathematics explained in depth.**

Commutative Property of Addition

Numerical Expression: 1+2= 2+1

Algebraic Expression: a+b= b+a

Shortcut: Even with changing the order of the factors, it does not change the ending result.

Associative Property of Multiplication

Numerical Expression: (1*2)*3= 1*(2*3)

Algebraic Expression: (a*b)*c= a*(b*c)

Shortcut: The multiplication of a set of numbers is the same regardless of how the numbers are grouped.

Commutative Property of Multiplication

Numerical Expression: 1*2= 2*1

Algebraic Expression: a*b= b*a

Shortcut: With changing the order of both factors, the product would still have the same ending result.

Identity Property of Addition

Need some help learning it?

Keyword:

social

-Think of the numbers as amounts of people. They can socialize with anyone they want in the group, yet there are still the same amount of people in the group.

Practice:

2 + (1 + 3) = ?

2 + (1 + 3) = (2 + 1) + 3

Numerical Expression: 1+0=1

Algebraic Expression: a+0=a

Shortcut: States that the sum of any number or variable and zerio is the number or variable itself.

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**Start**

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Learning in Depth

Keyword:

social

Socializing with the same amount

of people

Practice:

3 * (4 * 2) = ?

3 * (4 * 2) = (3 * 4) * 2

Try It Out

Keyword:

Commute

Think of a car, you can sit anywhere in the car, yet there are still the same amount of people in the car.

Practice

4 + 5 + 2 = ?

4 + 5 + 2 = 2 + 4 + 5

Need help learning it?

Keyword:

Commute- to travel

Think of the numbers as amounts of guests bringing friends with them to a party. If everyone brings 2 friends, it won't matter who you meet first, you will meet the same amount of people in the end.

Practice

3 * 2 * 4 = ?

3 * 2 * 4 = 2 * 4 * 3

More About the Property

Keyword:

Invert, reverse

Think of this property as a way of

reversing the number to turn

back into zero.

Practice

-5 + 5 = ?

-5 + 5 = 0

Reversing -5 to become 0

5 cancles out -5 to become 0

Need help?

Keyword:

Invert, reverse

Say you cut up 8 cookies each into

8 pieces, addressing each piece

as"1/8". If you put back together

8 of the pieces, you end up with

one whole cookie.

Practice

4 * 1/4 = ?

4 * 1/4 = 1

Going into Depth

Keyword:

Distribute

Think of having to buy a number of cookies to give to a number of people. Instead of counting them all at once, you can divide them into groups to make it easier to determine how many cookies you need to buy.

Practice

2 * (4 + 2) = ?

2 * (4 + 2) = 2(4)+2(2)

Understanding the Concept Better

Keyword:

Identity

Think of this property as trying to not change the identity of someone or something by choosing to not add anything when you are asked to do so.

Practice

2 + 0 = ?

2 + 0 = 2

Need some help?

Keyword:

Identiy

Let's say you made 10 cookies. It doesn't matter if for every 2 friends you give 5 cookies or every 5 friends 2 cookies, you are still giving 10 cookies away.

Practice

140 * 1 = ?

140 * 1 = 140

Does not affect 140

More About The Property

Keyword:

zero

Adding zero to a number will not change it in anyway. Multiplying a number by zero will change the value to become zero itself.

Practice

3 * 0 = ? 4 + 0 = ?

3 * 0 = 0 4 + 0 = 4