Chapter 1.2, Problem 2P

(a)

To determine

To find: the simplest form of an expression.

Answer to Problem 2P

  $5.7-4^2÷2=27$ .

Explanation of Solution

Given:

  $5.7-4^2÷2.$

Concept used:

In general, an expression is in simplest form when it is easiest to use.

Common ways to help it simplify is:

Combining like terms.

Factoring.

Expanding the opposite of factoring.

Clear out fractions by multiplying.

Recognizing the pattern and it has seen before, like the difference of squares etc.

Use bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ .

Calculation:

According to the given:

  $5.7-4^2÷2.$

Using bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ :

  $\begin{array}{l}5.7-4^2÷2.\\ \Rightarrow 35-8.\\ \Rightarrow 27.\end{array}$

Hence, $5.7-4^2÷2=27$ .

(b)

To determine

To find: the simplest form of an expression.

Answer to Problem 2P

  $12-25÷5=7$ .

Explanation of Solution

Given:

  $12-25÷5$ .

Concept used:

In general, an expression is in simplest form when it is easiest to use.

Common ways to help it simplify is:

Combining like terms.

Factoring.

Expanding the opposite of factoring.

Clear out fractions by multiplying.

Recognizing the pattern and it has seen before, like the difference of squares etc.

Use bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ .

Calculation:

According to the given:

  $12-25÷5$ .

Using bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ :

  $\begin{array}{l}12-25÷5.\\ \Rightarrow 12-5.\\ \Rightarrow 7.\end{array}$

Hence, $12-25÷5=7$ .

(c)

To determine

To find: the simplest form of an expression.

Answer to Problem 2P

  $\frac{4+3^4}{7-2}=17$ .

Explanation of Solution

Given:

  $\frac{4+3^4}{7-2}$ .

Concept used:

In general, an expression is in simplest form when it is easiest to use.

Common ways to help it simplify is:

Combining like terms.

Factoring.

Expanding the opposite of factoring.

Clear out fractions by multiplying.

Recognizing the pattern and it has seen before, like the difference of squares etc.

Use bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ .

Calculation:

According to the given:

  $\frac{4+3^4}{7-2}$ .

Using bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ :

  $\begin{array}{l}\frac{4+3^4}{7-2}.\\ \Rightarrow \frac{4+81}{5}.\\ \Rightarrow \frac{85}{5}=17.\end{array}$

Hence, $\frac{4+3^4}{7-2}=17$ .

(d)

To determine

To find: the reason for the fraction bar acts as grouping symbol.

Answer to Problem 2P

The order of operation tells to simplify the numerator and the denominator first as if there were in the parentheses before divide.

Explanation of Solution

Given:

Fraction bars act as grouping symbols.

Concept used:

Fraction bars act as grouping symbols. The expressions above and below the fraction bar should be treated as they were in the bracket or parentheses.

Use bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ .

Calculation:

Fraction bars act as grouping symbols. The expressions above and below the fraction bar should be treated as they were in the bracket or parentheses. The order of operation tells to simplify the numerator and the denominator first as if there were in the parentheses before divide.

Grouping symbols:

Parentheses	$\left(\right)$
Brackets	$\left[\right]$
Braces	$\left\{\right\}$
Absolute value	$\left|\right|$
Fraction bar	$\frac{\left(\right)}{\left(\right)}$

Hence, the order of operation tells to simplify the numerator and the denominator first as if there were in the parentheses before divide.