Complete the following table.

Numbers	Additive properties
	Closed	Commutative	Associative	Existence of identity	Existence of Inverse
Rational numbers	Yes
Integers	Yes
Whole numbers				Yes	No
Natural numbers	Yes

 

 

Complete the following table.

Name the property involved in the following example:

$\frac{8}{5}+0=\frac{8}{5}=0+\frac{8}{5}$

Name the property involved in the following example: [Closure property/ Commutative property/ Associative property/ Distributive property]

$2\left(\frac{3}{5}+\frac{1}{2}\right)=2\left(\frac{3}{5}\right)+2\left(\frac{1}{2}\right)$

Name the property involved in the following examples

$\frac{3}{7}\times 1=\frac{3}{7}=1\times \frac{3}{7}$

Name the property involved in the following examples

$\left(\frac{-2}{5}\right)\times 1=\frac{-2}{5}=1\times \left(\frac{-2}{5}\right)$

(Distributive Property/ Multiplicative Inverse/Additive Inverse/Multiplicative Identity).

Name the property involved in the following example:

$\frac{2}{5}+\frac{1}{3}=\frac{1}{3}+\frac{2}{5}$

(Commutative law of addition/Distributive law of addition/Associative law of addition)

The property involved in the following example is _____ property in multiplication:

$\frac{5}{2}\times \frac{3}{7}=\frac{15}{14}$

Name the property involved in the following example:

$7a + (-7a) = 0$