Q35. - Algebra 2

Question

Name the property illustrated by each equation. 

35. $ab=1ab$

Step-by-Step Solution

Answer

Name of the property illustrated is Multiplicative Identity.

Step 1 - Write properties of real numbers

Properties of real numbers are written in following table:

For any real numbers $a,b,$ and $c:$
Property	Addition	Multiplication
Commutative	$a+b=b+a$	$a·b=b·a$
Associative	$\left(a+b\right)+c=a+\left(b+c\right)$	$\left(a·b\right)·c=a·\left(b·c\right)$
Identity	$a+0=a=0+a$	$a·1=a=1·a$
Inverse	$a+\left(-a\right)=0=\left(-a\right)+a$	If $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$
Distributive	$a\left(b+c\right)=ab+ac\text{ and }\left(b+c\right)a=ba+ca$

Step 2 - Substitution in given values

Substitute $c$ for ab  in given equation

Now equation becomes $c=1·c$

Step 3 - Identify the property

From the table of properties of real numbers, $c=1·c$ is the property of identity in multiplication. 

Thus, multiplicative identity is illustrated by given equation.