Q7. - Algebra 2

Question

Name the property illustrated by each equation. 

$\frac{2}{3}·\frac{3}{2}=1$

Step-by-Step Solution

Answer

Name of the property illustrated is Multiplicative Inverse.

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 a for $\frac{2}{3}$ in given equation.

As, $\frac{3}{2}$ can be written as $\frac{1}{\frac{2}{3}}$. Replace $\frac{3}{2}$ with $\frac{1}{a}$ in the given equation

Now equation becomes $a·\frac{1}{a}=1$

Step 3 - Identify the property

From the table of properties of real numbers, $a·\frac{1}{a}=1$ is the property of multiplicative inverse.

Thus, multiplicative inverse is illustrated by given equation.