Chapter 1: Q56. (page 46)

If , $5 < a < 7 < b < 14$ then which of the following best defines $\frac{a}{b}$ .?
a. $\frac{5}{7} < \frac{a}{b} < \frac{1}{2}$ B. $\frac{5}{14} < \frac{a}{b} < \frac{1}{2}$ C. $\frac{5}{7} < \frac{a}{b} < 1$ D. $\frac{5}{14} < \frac{a}{b} < 1$

Short Answer

Expert verified

The statement that best defines $\frac{a}{b}$ is $\frac{5}{14} < \frac{a}{b} < 1$ .Therefore the option D is correct.

Step by step solution

- Description of step.

It is given that $5 < a < 7 < b < 14$ .

Therefore, it can be obtained that:

$\frac{1}{5} > \frac{1}{a} > \frac{1}{7} > \frac{1}{b} > \frac{1}{14}$

As $5 < a$ , therefore it can be obtained that:

$\frac{5}{14} < \frac{a}{14}$

As, $\frac{1}{14} < \frac{1}{b}$ , therefore it can be obtained that:

$\begin{array}{l} \frac{1}{14} < \frac{1}{b} \\ \frac{a}{14} < \frac{a}{b} \end{array}$

As, $\frac{5}{14} < \frac{a}{14}$ and $\frac{a}{14} < \frac{a}{b}$ , therefore it can be obtained that:

$\begin{matrix} \frac{5}{14} < \frac{a}{14} < \frac{a}{b} \\ \Rightarrow \frac{5}{14} < \frac{a}{b} \end{matrix}$

Therefore, it is obtained that $\frac{5}{14} < \frac{a}{b}$ .

- Description of step.

As $a < 7$ , therefore it can be obtained that:

$\frac{a}{b} < \frac{7}{b}$

As, $\frac{1}{b} < \frac{1}{7}$ , therefore it can be obtained that:

$\begin{array}{l} \frac{7}{b} < \frac{7}{7} \\ \frac{7}{b} < 1 \end{array}$

As, $\frac{a}{b} < \frac{7}{b}$ and $\frac{7}{b} < 1$ , therefore it can be obtained that:

$\begin{matrix} \frac{a}{b} < \frac{7}{b} < 1 \\ \Rightarrow \frac{a}{b} < 1 \end{matrix}$

Therefore, it is obtained that $\frac{a}{b} < 1$ .

- Description of step.

As, $\frac{a}{b} < 1$ and $\frac{5}{14} < \frac{a}{b}$ , therefore it can be written as:

$\frac{5}{14} < \frac{a}{b} < 1$

The statement that best defines ${\frac{a}{b}}^{}$ is $\frac{5}{14} < \frac{a}{b} < 1$ .

Therefore the option D is correct.

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If , $5 < a < 7 < b < 14$ then which of the following best defines $\frac{a}{b}$ .?
a. $\frac{5}{7} < \frac{a}{b} < \frac{1}{2}$ B. $\frac{5}{14} < \frac{a}{b} < \frac{1}{2}$ C. $\frac{5}{7} < \frac{a}{b} < 1$ D. $\frac{5}{14} < \frac{a}{b} < 1$

Short Answer

Step by step solution

- Description of step.

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If , 5<a<7<b<14then which of the following best defines ab.?a.57<ab<12 B. 514<ab<12 C. 57<ab<1 D. 514<ab<1

Short Answer

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One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

If , $5 < a < 7 < b < 14$ then which of the following best defines $\frac{a}{b}$ .?
a. $\frac{5}{7} < \frac{a}{b} < \frac{1}{2}$ B. $\frac{5}{14} < \frac{a}{b} < \frac{1}{2}$ C. $\frac{5}{7} < \frac{a}{b} < 1$ D. $\frac{5}{14} < \frac{a}{b} < 1$

- Description of step.

- Description of step.

- Description of step.