Chapter 7: Q29. (page 247)

Show that the proportions $\frac{a + b}{b} = \frac{c + d}{d}$ and $\frac{a}{b} = \frac{c}{d}$ are equivalent.

Short Answer

Expert verified

The given proportion is equivalent.

Step by step solution

Step 1. Given information.

The given proportion is,

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

Step 2. Formula used.

Two proportional are said to be equivalent, if one can be obtained from the other.

Step 3. Proof.

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

Two proportional are said to be equivalent if one can be obtained from the other.

Again, $\frac{a}{b} = \frac{c}{d}$

Adding 1 on both sides, doesn’t change the proportion.

$\begin{array}{l} \frac{a}{b} + 1 = \frac{c}{d} + 1 \\ \frac{a + b}{b} = \frac{c + d}{d} \end{array}$

Therefore, the given proportion is equivalent.

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Show that the proportions $\frac{a + b}{b} = \frac{c + d}{d}$ and $\frac{a}{b} = \frac{c}{d}$ are equivalent.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Formula used.

Step 3. Proof.

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Show that the proportions a+bb=c+dd and ab=cd are equivalent.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Formula used.

Step 3. Proof.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Show that the proportions $\frac{a + b}{b} = \frac{c + d}{d}$ and $\frac{a}{b} = \frac{c}{d}$ are equivalent.