Chapter 1.1, Problem 31E

(a)

To determine

To place: the correct symbol for $3\underset{\_}{}\frac{7}{2}$ .

Answer to Problem 31E

  $3<\frac{7}{2}$

Explanation of Solution

Given information:

Two numbers are given as $3$ and $\frac{7}{2}$ .

Formula used:

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

  $\frac{a}{b}<\frac{c}{d}$ if $a<c,b=d$

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

  $\frac{a}{b}>\frac{c}{d}$ if $a>c,b=d$

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

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

Calculation:

Consider the given numbers.

  $3$ and $\frac{7}{2}$

Now, multiply numerator and denominator of 3 by 2.

  $3=\frac{3\times 2}{1\times 2}=\frac{6}{2}$

Here, for $\frac{6}{2}$ and $\frac{7}{2}$ ,

  $6<7$

Hence, $\frac{6}{2}<\frac{7}{2}$

Therefore, $3<\frac{7}{2}$ .

(b)

To determine

To place: the correct symbol for $-3\underset{\_}{}-\frac{7}{2}$ .

Answer to Problem 31E

  $-3>-\frac{7}{2}$

Explanation of Solution

Given information:

Two numbers are given as $-3$ and $-\frac{7}{2}$ .

Formula used:

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

  $\frac{a}{b}<\frac{c}{d}$ if $a<c,b=d$

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

  $\frac{a}{b}>\frac{c}{d}$ if $a>c,b=d$

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

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

Calculation:

Consider the given numbers.

  $-3$ and $-\frac{7}{2}$

Now, multiply numerator and denominator of 3 by 2.

  $3=\frac{3\times 2}{1\times 2}=\frac{6}{2}$

Here, for $\frac{6}{2}$ and $\frac{7}{2}$ ,

  $6<7$

Hence, $\frac{6}{2}<\frac{7}{2}$

Therefore, $3<\frac{7}{2}$ .

So, $-3>-\frac{7}{2}$

(c)

To determine

To place: the correct symbol for $3.5\underset{\_}{}\frac{7}{2}$ .

Answer to Problem 31E

  $3.5=\frac{7}{2}$

Explanation of Solution

Given information:

Two numbers are given as $3.5$ and $\frac{7}{2}$ .

Formula used:

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

  $\frac{a}{b}<\frac{c}{d}$ if $a<c,b=d$

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

  $\frac{a}{b}>\frac{c}{d}$ if $a>c,b=d$

For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ .

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

Calculation:

Consider the given numbers.

  $3.5$ and $\frac{7}{2}$

Now, multiply numerator and denominator of 3.5 by 2.

  $3.5=\frac{3.5\times 2}{1\times 2}=\frac{7}{2}$

Here, for $\frac{7}{2}$ and $\frac{7}{2}$ ,

  $7=7$

Hence, $\frac{7}{2}=\frac{7}{2}$

Therefore, $3.5=\frac{7}{2}$ .