Question

What can you conclude from the given information.

Explain why$\frac{a}{b}=\frac{c}{d}$and$\frac{b}{a}=\frac{d}{c}$ are equivalent.

Short answer

Both proportion gives the same equationthat’s why it is equivalent.

Step-by-step solution

Step 1. Given information.

The given proportions are,

$\frac{a}{b}=\frac{c}{d}and\frac{a}{c}=\frac{b}{d}$.

$aandd$are called extreme and$bandc$ are called means.

Step 2. Now, from the means-extreme property.

Product of means and product of extremes are equal.

It is given$\frac{a}{b}=\frac{c}{d}and\frac{a}{c}=\frac{b}{d}$,

For the proportion$a:b::c:d$,

i.e$\frac{a}{b}=\frac{c}{d}$,

Step 3. For the proportionab=cd  .

Means-extremes property gives$ad=bc$,

Similarly,

Step 4. For the proportionac=bd  .

Means-extremes property gives, $ad=bc$

So, both the proportion gives the same equation.

Therefore, the given proportion is equivalent.