Question

Please give the answer fast​

Answer 1

According to the question we know that ⇒

• a = 2

• b = $\frac{-1}{2}$

• c = $\frac{-1}{4}$

So now we have to verify the properties using the given value.

a) The following property is the commutative property over addition.

Property ⇒

$a+b=b+a$

Verification ⇒

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

$\frac{4}{2} +\frac{-1}{2}=\frac{-1}{2} +\frac{4}{2}$

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

∴ $a+b=b+a$

b) The following property is associative property over addition.

Property ⇒

$a+(b+c)=(a+b)+c$

Verification ⇒

$2+(\frac{-1}{2}+\frac{-1}{4})=(2+\frac{-1}{2})+\frac{-1}{4}$

$2+(\frac{-2}{4}+\frac{-1}{4})=(\frac{4}{2} +\frac{-1}{2})+\frac{-1}{4}$

$2+ \frac{-3}{4}=\frac{3}{2} +\frac{-1}{4}$

$\frac{8}{4} +\frac{-3}{4} = \frac{6}{4} +\frac{-1}{4}$

$\frac{5}{4} = \frac{5}{4}$

∴ $a+(b+c)=(a+b)+c$

c) The following property is commutative property over subtraction.

Property ⇒

$a-b\neq b-a$

Verification ⇒

$2-\frac{-1}{2} \neq \frac{-1}{2} -2$

$\frac{4}{2} -\frac{-1}{2}\neq \frac{-1}{2}-\frac{4}{2}$

$\frac{5}{2} \neq \frac{-5}{2}$

∴ $a-b\neq b-a$

d) The following property is associative property over multiplication.

Property ⇒

$a*(b*c)=(a*b)*c$

Verification ⇒

$2*(\frac{-1}{2}*\frac{-1}{4})=(2*\frac{-1}{2} )*\frac{-1}{4}$

$2* \frac{1}{8} = -1*\frac{-1}{4}$

$\frac{1}{4} =\frac{1}{4}$

∴ $a*(b*c)=(a*b)*c$

e) The following property is distributive property over subtraction.

Property ⇒

$a*(b-c)=(a*b)-(a*c)$

Verification ⇒

$2*(\frac{-1}{2} -\frac{-1}{4})=2*\frac{-1}{2} - 2*\frac{-1}{4}$

$2*(\frac{-2}{4}-\frac{-1}{4})=-1-\frac{-1}{2}$

$2*\frac{-1}{4} = \frac{-2}{2}-\frac{-1}{2}$

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

∴ $a*(b-c)=(a*b)-(a*c)$