Question

Write all properties of rational number with examples. Distributive property​

Answer 1

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→The properties of rational numbers are:

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

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Closure property→

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

Commutative Property→

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.

Associative Property→

→ 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

Distributive Property→

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 Property→

Examples:

1/2 + 0 = 1/2 [Additive Identity]

1/2 x 1 = 1/2 [Multiplicative Identity]

Inverse Property→

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

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Answer 2

Answer:

I have explained step by step

Step-by-step explanation:

This is the 2/3 + 1/6 = 1/6 + 2/3 = 5/6.

 8/3 × (7/6 × 5/4) = 35/9,

(8/3 × 7/6) × 5/4.

 (8/3 × 7/6) × 5/4

The major properties of properties of rational number are: Commutative, Associative, Distributive and Closure property.

Distributive property​ properties

Expand the equation.

Multiply (distribute) the primary numbers of every set, outer numbers of every set, inner numbers of every set, and therefore the last numbers of every set. Combine like terms.

8 × ( 20 + 7 ) = 8 × 20 + 8 × 7 = 160 + 56 = 216