Question

Explanate the formulas of :-

a) closure property of addition
b) commutative property of addition
c) associative property of addition

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Answer 1

Answer:

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Step-by-step explanation:

$\bold\red{Closure} \: \: \bold\red{ Property}$

The sum of the addition of two or more whole numbers is always a whole number.

Whole Number + Whole Number = Whole Number

For example, 2 + 4 = 6

Here, both 2 and 4 whole numbers and their sum is 6, which also is a whole number.

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$\bold\green{Commutative \: \: Property}$

When we add two or more whole numbers, their sum is the same regardless of the order of the addends.

Example 1: 2 + 4 = 4 + 2 = 6

The sum of both 2 + 4 and 4 + 2 is 6. That means, we can add whole numbers in any order.

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$\bold\pink{Associative \: \: Property}$

When three or more numbers are added, the sum is the same regardless of the grouping of the addends.

For example (4 + 2) + 3 = (4 + 3) + 2

Here, the addends are 2, 4 and 3. So, as per the associative property, the sum of the three numbers will remain the same, no matter how we group them.

Answer 2

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Answer:

●Closure property of Addition:

Consider the addition of (-5/14) and (-3/4) . The LCM of 14 and 4 is 28

(-5/14)+(-3/4) = {(-10+(-21)}/28 = (-31/28)

This means that, the sum of two rational numbers is also a rational number.

This is called closure property and we say that rational number are closed under addition.

In general , If a/b and c/d are two rational numbers , Then their sum (a/b + c/d) is also a rational number.

Then, Commutative property of addition.

Consider the numbers (2/5) and (4/15). The LCM of 5 and 15 is 15.

2/5+4/15 = {(2×3)+4)/15 = 10/15 = 2/3

Add the same number in reverse order. That is (4/15) and (2/5). The LCM is 15.

4/15 + 2/5 = {4 + (2×3)}/15 = (4+6)/15 = 2/3

The sum remains the same even if the order of the rational numbers is changed. This is called commutative property and we say that addition of rational numbers is commutative.

In general, if a/b and c/d are two rational number then a/b + c/d = c/d + a/b