Chapter 1.1, Problem 32E

(a)

To determine

To place: the correct symbol for $\frac{2}{3}\underset{\_}{}0.67$ .

Answer to Problem 32E

  $\frac{2}{3}<0.67$

Explanation of Solution

Given information:

Two numbers are given as $\frac{2}{3}$ and $0.67$ .

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.

  $\frac{2}{3}$ and $0.67$ .

Now, multiply numerator and denominator of 0.67 by 3.

  $0.67=\frac{0.67\times 3}{1\times 3}=\frac{2.01}{3}$

Here, for $\frac{2}{3}$ and $\frac{2.01}{3}$ ,

  $2<2.01$

Hence, $\frac{2}{3}<\frac{2.01}{3}$

Therefore, $\frac{2}{3}<0.67$ .

(b)

To determine

To place: the correct symbol for $\frac{2}{3}\underset{\_}{}-0.67$ .

Answer to Problem 32E

  $\frac{2}{3}>-0.67$

Explanation of Solution

Given information:

Two numbers are given as $\frac{2}{3}$ and $-0.67$ .

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.

  $\frac{2}{3}$ and $-0.67$ .

Now, multiply numerator and denominator of $0.67$ by 3.

  $0.67=\frac{0.67\times 3}{1\times 3}=\frac{2.01}{3}$

Here, for $\frac{2}{3}$ and $\frac{2.01}{3}$ ,

  $2<2.01$

Hence, $\frac{2}{3}<\frac{2.01}{3}$

So, $\frac{2}{3}>-0.67$

(c)

To determine

To place: the correct symbol for $0.67\underset{\_}{}\left|-0.67\right|$ .

Answer to Problem 32E

  $0.67=\left|-0.67\right|$

Explanation of Solution

Given information:

Two numbers are given as $0.67$ and $\left|-0.67\right|$ .

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.

  $0.67$ and $\left|-0.67\right|$

Now, $\left|-0.67\right|=0.67$ as $\left|-a\right|=a$