Question

Can anyone help to to understand all the given properties in mathematics

•closusre property
•commutative property
•Associative property
and
•Distributive property

Plzzzzzz do it yrr try to understand tomorrow is my maths exam:')​

Answer 1

(1) Closure Property - The closure property means that a set is closed for some mathematical operation. ... For example, the set of even natural numbers, [2, 4, 6, 8, . . .], is closed with respect to addition because the sum of any two of them is another even natural number, which is also a member of the set.

-> Formula - Closure property for addition : If a and b are two whole numbers and their sum is c, i.e. a + b = c, then c is will always a whole number. For any two whole numbers a and b, (a + b) is also a whole number. This is called the Closure-Property of Addition for the set of W.

(2) Commutative Property - The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.

-> Formula - The commutative property of multiplication tells us that it doesn't matter in what order you multiply numbers. The formula for this property is a * b = b * a. For example, it doesn't matter if we multiply 5 * 4 or 4 * 5.

(3) The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.

-> Associative Property of Addition

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

-> Associative Property of.

Multiplication

(a × b) × c = a × (b × c)

(4) The distributive property lets you multiply a sum by multiplying each addend separately and then add the products. ... Consider the first example, the distributive property lets you "distribute" the 5 to both the 'x' and the '2'.........

#Jai Mahakal.......

Answer 2

Answer:

$\huge\blue{Closusre.. Property:-}$

➡System of whole numbers is closed under multiplication, this means that the product of any two whole numbers is always a whole number. This is known as Closure Property for Multiplication of Whole Numbers.

➡. If you add two real numbers, you will get another real number. There is no possibility of ever getting anything other than another real number.

➡The set of real numbers is NOT closed under division.

3 ÷ 0 = undefined

Since "undefined" is not a real number, closure fails.

Division by zero is the ONLY case where closure fails for real numbers.

$\huge\red{Commutative... Property :-}$

The Commutative Property is the one that refers to moving stuff around.

➡ For addition, the rule is "a + b = b + a" in numbers, this means 2 + 3 = 3 + 2.

➡For multiplication, the rule is "ab = ba" in numbers, this means 2×3 = 3×2.

$\huge\blue{Associate.. Property:-}$

➡Whatever numbers a, b, and c may be, they always end up the same:

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

➡First, try to calculate (2 x 3) x 4. After, try 2 x (3 x 4). Did you get the same answer for both of them? this is associate Property of multiplication!

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

If a= 3, b= 5 y c = 10, we’re left with:

(3 x 5) x 10 = 15 x 10 =150

3 x (5 x 10) = 3 x 50 = 150

(3 x 10) x 5 = 30 x 5 = 150

$\huge\red{Distributive... Property:-}$

➡property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of the products – in this case, 6(5) – 6(2).

For example, suppose you want to multiply 3 by the sum of 10 + 2. According to this property, you can add the numbers and then multiply by 3.

#Read Carefully Dear and Gud Luck For Your exam !!