Question

mention the commutativity associativity and distributive property of rational number also check a × b is equal to b × a and a + b is equal to b + a for a equal to 3\2 and b is equal to 3 \4​

Answer 1

AnswEr :-

✦ Commutativity property

⇒ This property states that changing the order of the operands does not change the result.

For addition, the rule is a + b = b + a

$\boxed {\sf {2 + 3 = 3 + 2}}$

For multiplication, the rule is a × b = b × a

$\boxed {\sf {2 \times 3 = 3 \times 2}}$

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✦ Associativity property

⇒ This property states that numbers can be added or multiplied regardless of how the numbers are grouped.

For addition, the rule is a + (b + c) = (a + b) + c

$\boxed {\sf {1 + (2+3)=(1+2)+3}}$

For multiplication, the rule is a × (b × c) = (a × b) × c

$\boxed {\sf {2 \times (3 \times 4)=(2 \times 3) \times 4 }}$

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✦ Distributive property

⇒ This property states that multiplying the sum of addends by a number will give the same result as multiplying each addend individually by the number and then adding all the products.

For multiplication, the rule is (a × b) + (a × c) = a × (b + c)

$\boxed {\sf {(3 \times 2)+(3 \times 4) = 3 \times (2+4)}}$

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SoluTion :-

$\sf {a \times b = b \times a}\\\\\\\\\sf {\dfrac{3}{2} \times \dfrac{3}{4} = \dfrac{3}{4} \times \dfrac{3}{2}}\\\\\\\sf {\dfrac{9}{8} =\dfrac{9}{8} }$

Since, LHS = RHS

Hence, Proved

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$\sf {a+b=b+a}\\\\\\\\\sf {\dfrac{3}{2} + \dfrac{3}{4} =\dfrac{3}{4} + \dfrac{3}{2}}\\\\\\\sf {\dfrac{6}{4} + \dfrac{3}{4} =\dfrac{3}{4} + \dfrac{6}{4}}\\\\\\\sf {\dfrac{9}{4} =\dfrac{9}{4} }$

Since, LHS = RHS

Hence, Proved