Question

what is Closure Property, Associative Property, Commutative Property& Distributive Property ?.
how to use it ?.
explain in 50 words.
will get brainliest.
​

Answer 1

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Distributive Property: 5 Clear Examples to Use in Class

June 14, 2019

Jordan Nisbet

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What is the distributive property? Also known as the distributive law of multiplication, it’s one of the most commonly used properties in mathematics.

When you distribute something, you are dividing it into parts. In math, the distributive property helps simplify difficult problems because it breaks down expressions into the sum or difference of two numbers.

Looking for a specific operation? Click the highlighted tabs and jump right to the:

Definition of distributive property

Distributive property of addition

Distributive property of subtraction

Distributive property of variables

Distributive property of exponents

Distributive property of fractions

Engaging ways to teach distributive property

Distributive property definition

For expressions in the form of a(b+c), the distributive property shows us how to solve them by:

Multiplying the number immediately outside parentheses with those inside

Adding the products together

What is the distributive property

What about PEMDAS? What happened to first evaluating what’s inside parentheses?

If your students are wondering why you aren’t following the order of operations you’ve taught them in the past, they’re not wrong.

However, when algebraic expressions have parentheses containing variables -- a quantity that may change within the context of a mathematical problem, usually represented by a single letter -- performing that operation isn’t possible.

Distributive property of multiplication over addition

Regardless of whether you use the distributive property or follow the order of operations, you’ll arrive at the same answer. In the first example below, we simply evaluate the expression according to the order of operations, simplifying what was in parentheses first.

Distributive property of addition

Using the distributive law, we:

Multiply, or distribute, the outer term to the inner terms.

Combine like terms.

Solve the equation.

Distributive property multiplication

Let’s use a real-life scenario to help make this clearer.

Imagine one student and her two friends each have seven strawberries and four clementines. How many pieces of fruit do all three students have in total?

In their lunch bags -- or, the parentheses -- they each have 7 strawberries and 4 clementines. To know the total number of pieces of fruit, they need to multiply the whole thing by 3.

When you break it down, you’re multiplying 7 strawberries and 4 clementines by 3 students. So, you end up with 21 strawberries and 12 clementines, for a total of 33 pieces of fruit.

Distributive property of multiplication over subtraction

Similar to the operation above, performing the distributive property with subtraction follows the same rules -- except you’re finding the difference instead of the sum.

Distributive property problems

Note: It doesn’t matter if the operation is plus or minus. Keep whichever one is in the parentheses.

Distributive property with variables

Remember what we said about algebraic expressions and variables? The distributive property allows us to simplify equations when dealing with unknown values.

Using the distributive law with variables involved, we can isolate x:

Multiply, or distribute, the outer term to the inner terms.

Combine like terms.

Arrange terms so constants and variables are on opposite sides of the equals sign.

Solve the equation and simplify, if needed.

How to do distributive property

Answer 2

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Closure property :-

A set that is closed under an operation is said to satisfy a closure property.

Example - When we add a whole number, the result is always a whole number like 2+3 = 5 (whole number)

Commutative property :-

The commutative property says that the order in which we multiply/add the numbers in any orders does not change the result.

Example - 2+3 = 5 and 3+2 is also 5.

Associative property :-

The associative property says that the way in which factors are grouped in addition/multiplication, the problem does not change the product.

Example - (2+3)+2 = 7 = 2+(3+2)

Distributive property :-

In distributive property, by multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Example - 4(3+2) = 4×5 = 20

And by this property,

4(3+2) = 4×3 + 4×2 = 12+8 = 20