Chapter P, Problem 1E

Exercises

You can use the following problems as a self-test on the material presented in this review. If you can handle these problems, you’re ready to do all of the arithmetic in this text. If you have difficulty with any of these problems, please review the appropriate section of this prologue. You might also want to use this section as an opportunity to become more familiar with your calculator. The answers are given immediately following these exercises, along with commentary and some reminders.

Complete each of the following:

a. $17\times 3=$

b. $17(3)=$

c. $\left(17\right)(3)=$

d. $17/3=$

e. ${(42)}^2=$

f. $\sqrt{113}=$

To determine

a.

To compute:

The given expression.

Answer to Problem 1E

Solution:

The value of the expression $17\times 3$ is 51.

Explanation of Solution

Given:

The expression is $17\times 3$.

Approach:

Multiplication:

A mathematical operation performed on a pair of numbers in order to derive a third number

called a product.

The operation of multiplying some number a by some number b may be symbolized in six

different ways:

$a\times b$

$a\cdot b$

$a*b$

$ab$

$a(b)$

$(a)(b)$

Calculation:

The given expression is $17\times 3$.

Here, the symbol $\times$ represents multiplication. We have to multiply 17 by 3 times, we get 51.

(i.e.,) $17\times 3=51$.

Final statement:

Therefore, the value of the expression $17\times 3$ is 51.

To determine

b.

To compute:

The given expression.

Answer to Problem 1E

Solution:

The value of the expression $17(3)$ is 51.

Explanation of Solution

Given:

The expression is $17(3)$.

Approach:

Multiplication:

A mathematical operation performed on a pair of numbers in order to derive a third number

called a product.

The operation of multiplying some number a by some number b may be symbolized in six

different ways:

$a\times b$

$a\cdot b$

$a*b$

$ab$

$a(b)$

$(a)(b)$

Calculation:

The given expression is $17(3)$.

Here, the brackets represents multiplication. We have to multiply 17 by 3 times, we get 51.

(i.e.,) $17\left(3\right)=51$.

Final statement:

Therefore, the value of the expression $17(3)$ is 51.

To determine

c.

To compute:

The given expression.

Answer to Problem 1E

Solution:

The value of the expression $\left(17\right)(3)$ is 51.

Explanation of Solution

Given:

The expression is $\left(17\right)(3)$.

Approach:

Multiplication:

A mathematical operation performed on a pair of numbers in order to derive a third number

called a product.

The operation of multiplying some number a by some number b may be symbolized in six

different ways:

$a\times b$

$a\cdot b$

$a*b$

$ab$

$a(b)$

$(a)(b)$

Calculation:

The given expression is $\left(17\right)(3)$.

Here, the brackets represents multiplication. We have to multiply 17 by 3 times, we get 51.

(i.e.,) $(17)\left(3\right)=51$.

Final statement:

Therefore, the value of the expression $\left(17\right)(3)$ is 51.

To determine

d.

To compute:

The given expression.

Answer to Problem 1E

Solution:

The value of the expression $17/3$ is $5.67$.

Explanation of Solution

Given:

The expression is $17/3$.

Approach:

Division:

The operation of division can also be expressed in several different ways as follows,

$a/b\text{or}\frac{a}{b}$.

Calculation:

The given expression is $17/3$.

Here, the symbol “$/$” represents division.

Hence, we have to divide 17 by 3.

We get $\mathrm{5.66666...}$

To round off, look at the digit in ${1000}^{th}$ place.

Since, the digit is greater than 5, round up it as $5.67$.

Thus, the value of the given expression $17/3$ is $5.67$.

Final statement:

The value of the expression $17/3$ is $5.67$.

To determine

e.

To compute:

The given expression.

Answer to Problem 1E

Solution:

The value of the expression ${\left(42\right)}^2$ is $1764$.

Explanation of Solution

Given:

The expression is ${\left(42\right)}^2$.

Approach:

Square of a number:

Square of a number is to multiply the number by itself. This operation is symbolized as $X^2$, which is the same thing as (X)(X).

Calculation:

The given expression is ${\left(42\right)}^2$.

We know that, $X^2=\left(X\right)\left(X\right)$

Substitute $X=42$ in the above expression,

$\begin{array}{rll}{\left(42\right)}^2& =& \left(42\right)\left(42\right)\\ {\left(42\right)}^2& =& 1764\end{array}$

Hence 42 squared is $1764$.

i.e., ${\left(42\right)}^2=1764$.

Final statement:

The value of the expression ${\left(42\right)}^2$ is $1764$.

To determine

f.

To compute:

The given expression.

Answer to Problem 1E

Solution:

The value of the expression $\sqrt{113}$ is $10.63$.

Explanation of Solution

Given:

The expression is $\sqrt{113}$.

Approach:

Square root of a number:

The square root of a number is the value that, when multiplied by itself, results in the original number. This operation is symbolized as $\sqrt{X}$.

Calculation:

The given expression is $\sqrt{113}$.

Here, the symbol “$\sqrt{}$” represents square root.

Hence, we have to find the square root of the number $113$.

We get $\mathrm{10.63014...}$

To round off, look at the digit in ${1000}^{th}$ place.

Since, the digit is less than 5 round down it as $10.63$.

Thus, the value of the given expression $\sqrt{113}$ is $10.63$.

Final statement:

The value of the expression $\sqrt{113}$ is $10.63$.