Exercise: Properties of Real Numbers

This illustrates the Multiplicative Inverse, which says that a number combined with its inverse results in the identity value.

For example: $a \times \dfrac{1}{a} = 1$

This demonstrates the Commutative Property: changing the order of the terms does not change the result for $*$.

$c * s$ is equal to $s * c$.

This is an example of the Additive Identity, which states that combining any number with the identity value leaves the number unchanged.

It matches the pattern: $a + 0 = a$ or $0 + a = a$.

This matches the pattern of the Distributive Property:$a(b + c) = ab + ac$ or$(b + c)a = ba + ca$.

When extended to three terms, it follows:$a(b + c + d) = ab + ac + ad$.

This matches the pattern of the Distributive Property:$a(b + c) = ab + ac$ or$(b + c)a = ba + ca$.

This matches the pattern of the Distributive Property:$a(b + c) = ab + ac$ or$(b + c)a = ba + ca$.

This is an example of the Additive Identity, which states that combining any number with the identity value leaves the number unchanged.

It matches the pattern: $a + 0 = a$ or $0 + a = a$.

This illustrates the Additive Inverse, which says that a number combined with its inverse results in the identity value.

For example: $a + (-a) = 0$

This illustrates the Multiplicative Inverse, which says that a number combined with its inverse results in the identity value.

For example: $a \times \dfrac{1}{a} = 1$

This matches the pattern of the Distributive Property:$a(b + c) = ab + ac$ or$(b + c)a = ba + ca$.

When extended to three terms, it follows:$a(b + c + d) = ab + ac + ad$.

This follows the Associative Property: changing the grouping of terms does not change the result.

It matches the structure: $(a * b) * c = a * (b * c)$

This follows the Associative Property: changing the grouping of terms does not change the result.

It matches the structure: $(a * b) * c = a * (b * c)$

This demonstrates the Commutative Property: changing the order of the terms does not change the result for $+$.

$\left(-\sqrt{7}\right) + y$ is equal to $y + \left(-\sqrt{7}\right)$.

This illustrates the Multiplicative Inverse, which says that a number combined with its inverse results in the identity value.

For example: $a \times \dfrac{1}{a} = 1$

This demonstrates the Commutative Property: changing the order of the terms does not change the result for $+$.

$\left(-\dfrac{4}{10}\right) + n$ is equal to $n + \left(-\dfrac{4}{10}\right)$.