Question

define closure property with example and verify is it satisfy under addition, subtraction, multiplication and division​

Answer 1

Answer:

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. For example:

3+4=7 which is also a whole number.

But 3−4=−1 which is not a whole number.

So, the property of closure for subtraction is not always true.

Closure property for multiplication :

If a and b are whole numbers then their multiplication is also a whole number.

For any two whole numbers a and b, (a×b) is also a whole number.For example:

30×7=210 which is also a whole number.

But property of closure is not always true for division. For example:

45÷0= not defined

As division with zero is not possible.

Hence, closure property is satisfied in whole numbers w.r.t. to addition and multiplication.

Step-by-step explanation:

please mark my answer as brainlist

Answer 2

1️⃣Closure property

For two rational numbers say x and y the results of addition, subtraction and multiplication operations give a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication.

For example:

1. (7/6)+(2/5) = 47/30
2. (5/6) – (1/3) = 1/2
3. (2/5). (3/7) = 6/35

NOTE :

The division is not under closure property because division by zero is not defined. We can also say that except ‘0’ all numbers are closed under division.

TO MORE INFORMATION :

What are the properties of rational numbers?

The word rational has evolved from the word ratio. In general, rational numbers are those numbers that can be expressed in the form of p/q, in which both p and q are integers and q≠0. The properties of rational numbers are

• Closure Property
• Commutative Property
• Associative Property
• Distributive Property
• Identity Property
• Inverse Property

2️⃣Commutative Property

For rational numbers, addition and multiplication are commutative.

Commutative law of addition: a+b = b+a

Commutative law of multiplication: a×b = b×a

For example:

$\frac{2}{5} \times \frac{3}{7} = \frac{3}{7} \times \frac{2}{5} = \frac{6}{35}$

Subtraction is not commutative property i.e. a-b ≠ b-a. This can be understood clearly with the following example:

$\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$

Whereas,

$\frac{1}{3} - \frac{2}{3} = - \frac{1}{3}$

The division is also not commutative i.e. a/b ≠ b/a, since,

$\frac{4}{9} \div \frac{1}{2} = \frac{8}{9}$

Whereas,

$\frac{1}{2} \div \frac{4}{9} = \frac{9}{8}$

3️⃣Associative Property

Rational numbers follow the associative property for addition and multiplication.

Suppose x, y and z are rational, then for addition: x+(y+z)=(x+y)+z

For multiplication: x(yz)=(xy)z.

Example: 1/2 + (1/4 + 2/3) = (1/2 + 1/4) + 2/3

⇒ 17/12 = 17/12

And in case of multiplication;

1/2 x (1/4 x 2/3) = (1/2 x 1/4) x 2/3

⇒ 2/24 = 2/24

⇒1/12 = 1/12

4️⃣Distributive Property

The distributive property states, if a, b and c are three rational numbers, then;

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

Example: 1/2 x (1/2 + 1/4) = (1/2 x 1/2) + (1/2 x 1/4)

LHS = 1/2 x (1/2 + 1/4) = 3/8

RHS = (1/2 x 1/2) + (1/2 x 1/4) = 3/8

Hence, proved

Identity and Inverse Properties of Rational Numbers

5️⃣Identity Property:

0 is an additive identity and 1 is a multiplicative identity for rational numbers.

Examples:

• 1/2 + 0 = 1/2 [Additive Identity]
• 1/2 x 1 = 1/2 [Multiplicative Identity]

6️⃣Inverse Property:

For a rational number x/y, the additive inverse is -x/y and y/x is the multiplicative inverse.

Examples:

The additive inverse of 1/3 is -1/3. Hence, 1/3 + (-1/3) = 0

The multiplicative inverse of 1/3 is 3. Hence, 1/3 x 3 = 1