CMIIh

2021-08-15

To explain: Whether all the proportions yield the same result.
a. $\frac{x}{2}=\frac{4}{9}$.
b. $\frac{2}{x}=\frac{9}{4}$.
c. $\frac{x}{4}=\frac{2}{9}$
d. $\frac{9}{2}=\frac{4}{x}$
e. $\frac{4}{9}=\frac{x}{2}$

Definition used:
"A rational equation that involves two ratios is called a proportion".
Theorem used:
Means-Extremes Theorem
"If $\frac{a}{b}=\frac{c}{d}$, where $b\ne 0$ and $d\ne 0$, then $ad=bc$.
Calculation:
Consider the proportion a. $\frac{x}{2}=\frac{4}{9}$
Simplify the proportion $\frac{x}{2}=\frac{4}{9}$ as follows.
$\frac{x}{2}=\frac{4}{9}$
$x\cdot 9=4\cdot 2$ [Cross multiply]
$9x=8$
$\frac{9x}{9}=\frac{8}{9}$ [Divide both the sides with 9]
$x=\frac{8}{9}$
Consider the proportion b. $\frac{2}{x}=\frac{9}{4}$.
Simplify the proportion $\frac{2}{x}=\frac{9}{4}$ as follows.
$\frac{2}{x}=\frac{9}{4}$
$x\cdot 9=4\cdot 2$ [Cross multiply]
$9x=8$
$\frac{9x}{9}=\frac{8}{9}$ [Divide both the sides with 9]
$x=\frac{8}{9}$
Consider the proportion c. $\frac{x}{4}=\frac{2}{9}$
Simplify the proportion $\frac{x}{4}=\frac{2}{9}$ as follows.
$\frac{x}{4}=\frac{2}{9}$
$x\cdot 9=4\cdot 2$ [Cross multiply]
$9x=8$
$\frac{9x}{9}=\frac{8}{9}$ [Divide both the sides with 9]
$x=\frac{8}{9}$
Consider the proportion d. $\frac{9}{2}=\frac{4}{x}$
Simplify the proportion $\frac{9}{2}=\frac{4}{x}$ as follows.
$\frac{9}{2}=\frac{4}{x}$
$x\cdot 9=4\cdot 2$ [Cross multiply]
$9x=8$
$\frac{9x}{9}=\frac{8}{9}$ [Divide both the sides with 9]
$x=\frac{8}{9}$
Consider the proportion e. $\frac{4}{9}=\frac{x}{2}$.
Simplify the proportion $\frac{4}{9}=\frac{x}{2}$ as follows.
$\frac{4}{9}=\frac{x}{2}$
$x\cdot 9=4\cdot 2$ [Cross multiply]
$9x=8$

Jeffrey Jordon