Chapter 7: Q16. (page 246)

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

Expert verified

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

Step by step solution

Step 1. Given information.

The given proportions are,

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

$a a n d d$ are called extreme and $b a n d c$ are called means.

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

Product of means and product of extremes are equal.

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

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 $a d = b c$ ,

Similarly,

Step 4. For the proportionac=bd .

Means-extremes property gives, $a d = b c$

So, both the proportion gives the same equation.

Therefore, the given proportion is equivalent.

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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

Step by step solution

Step 1. Given information.

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

Step 3. For the proportionab=cd .

Step 4. For the proportionac=bd .

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What can you conclude from the given information.Explain whyab=cdandba=dc are equivalent.

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. For the proportionab=cd .

Step 4. For the proportionac=bd .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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.