Chapter 1

Evaluate each expression. \(\frac{(-2)^{2}-4}{4-9}\)

Each calculation below is incorrect. Find the error and correct it. $$ 9-(-7) \stackrel{?}{=} 2 $$

Are parentheses necessary in the expression \(2+(3 \cdot 5) ?\) Explain your answer.

Evaluate each expression. \(\frac{6-2(-3)}{4-3(-2)}\)

Each calculation below is incorrect. Find the error and correct it. $$ -4-8 \stackrel{?}{=} 4 $$

Are parentheses necessary in the expression \((2+3) \cdot 5 ?\) Explain your answer.

Evaluate each expression. \(\frac{8-3(-2)}{2-5(-4)}\)

Each calculation below is incorrect. Find the error and correct it. $$ 10-30 \stackrel{?}{=} 20 $$

Evaluate each expression. \(\frac{|5-9|+|10-15|}{|2(-3)|}\)

Each calculation below is incorrect. Find the error and correct it. $$ -3-(-10) \stackrel{?}{=}-13 $$

Match each expression in the first column with its value in the second column. a. \((1+4) \cdot 6-3\) 15 b. \(1+4 \cdot(6-3)\) 13 c. \(1+4 \cdot 6-3\) 27 d. \((1+4) \cdot(6-3)\) 22

Evaluate each expression. \(\frac{|-3+6|+|-2+7|}{|-2 \cdot 2|}\)

If \(p\) is a positive number and \(n\) is a negative number, determine whether each statement is true or false. Explain your answer. $$ p-n \text { is always a positive number. } $$

Recall that perimeter measures the distance around a plane figure and area measures the amount of surface of a plane figure. The expression \(2 l+2 w\) gives the perimeter of the rectangle below (measured in units), and the expression lw gives its area (measured in square units). Complete the chart below for the given lengths and widths. Be sure to include units. $$ \begin{array}{|l|c|c|c|} \hline \text { Length: } I & \text { Width: } \boldsymbol{w} & \begin{array}{c} \text { Perimeter of } \\ \text { Rectangle: } \\ \mathbf{2 I}+\mathbf{2 w} \end{array} & \begin{array}{c} \text { Area of } \\ \text { Rectangle: } \\ \boldsymbol{I} \boldsymbol{w} \end{array} \\ \hline 4 \text { in. } & 3 \text { in. } & & \\ \hline \end{array} $$

Name 2 numbers whose sum is -17 .

Evaluate each expression. \(\frac{-7(-1)+(-3) 4}{(-2)(5)+(-6)(-8)}\)

If \(p\) is a positive number and \(n\) is a negative number, determine whether each statement is true or false. Explain your answer. $$ n-p \text { is always a negative number. } $$

Recall that perimeter measures the distance around a plane figure and area measures the amount of surface of a plane figure. The expression \(2 l+2 w\) gives the perimeter of the rectangle below (measured in units), and the expression lw gives its area (measured in square units). Complete the chart below for the given lengths and widths. Be sure to include units. $$ \begin{array}{|l|c|c|c|} \hline \text { Length: } I & \text { Width: } \boldsymbol{w} & \begin{array}{c} \text { Perimeter of } \\ \text { Rectangle: } \\ \mathbf{2 I}+\mathbf{2 w} \end{array} & \begin{array}{c} \text { Area of } \\ \text { Rectangle: } \\ \boldsymbol{I} \boldsymbol{w} \end{array} \\ \hline 6 \text { in. } & 1 \text { in. } & & \\ \hline \end{array} $$

Name 2 numbers whose sum is -30

Evaluate each expression. \(\frac{8(-7)+(-2)(-6)}{(-9)(3)+(-10)(-11)}\)

Recall that perimeter measures the distance around a plane figure and area measures the amount of surface of a plane figure. The expression \(2 l+2 w\) gives the perimeter of the rectangle below (measured in units), and the expression lw gives its area (measured in square units). Complete the chart below for the given lengths and widths. Be sure to include units. $$ \begin{array}{|l|c|c|c|} \hline \text { Length: } I & \text { Width: } \boldsymbol{w} & \begin{array}{c} \text { Perimeter of } \\ \text { Rectangle: } \\ \mathbf{2 I}+\mathbf{2 w} \end{array} & \begin{array}{c} \text { Area of } \\ \text { Rectangle: } \\ \boldsymbol{I} \boldsymbol{w} \end{array} \\ \hline 5.3 \text { in. } & 1.7 \text { in. } & & \\ \hline \end{array} $$

If \(p\) is a positive number and \(n\) is a negative number, determine whether each statement is true or false. Explain your answer. $$ |n-p| \text { is always a positive number. } $$

Recall that perimeter measures the distance around a plane figure and area measures the amount of surface of a plane figure. The expression \(2 l+2 w\) gives the perimeter of the rectangle below (measured in units), and the expression lw gives its area (measured in square units). Complete the chart below for the given lengths and widths. Be sure to include units. $$ \begin{array}{|l|c|c|c|} \hline \text { Length: } I & \text { Width: } \boldsymbol{w} & \begin{array}{c} \text { Perimeter of } \\ \text { Rectangle: } \\ \mathbf{2 I}+\mathbf{2 w} \end{array} & \begin{array}{c} \text { Area of } \\ \text { Rectangle: } \\ \boldsymbol{I} \boldsymbol{w} \end{array} \\ \hline 4.6 \text { in. } & 2.4 \text { in. } & & \\ \hline \end{array} $$

Each calculation below is incorrect. Find the error and correct it. See the Concept Check in this section. $$ -4+14 \stackrel{?}{=}-18 $$

Name the property illustrated by each step. $$ \text { a. }(x+y)+z=x+(y+z) $$ $$ \text { b. } \quad=(y+z)+x $$ $$ \text { c. } \quad=(z+y)+x $$

Each calculation below is incorrect. Find the error and correct it. See the Concept Check in this section. $$ -10+(-12) \stackrel{?}{=}-120 $$

Explain why 0 is called the identity element for addition.

Without calculating, determine whether each answer is positive or negative. Then use a calculator to find the exact difference. $$ 4.362-7.0086 $$

In your own words, explain the difference between an expression and an equation.

Each calculation below is incorrect. Find the error and correct it. See the Concept Check in this section. $$ -15+(-17) \stackrel{?}{=} 32 $$

Explain why 1 is called the identity element for multiplication.

Insert one set of parentheses so that the following expression simplifies to 32 . $$ 20-4 \cdot 4 \div 2 $$

For Exercises 107 through 110 , determine whether each statement is true or false. The sum of two negative numbers is always a negative number.

Write an example that shows that division is not commutative.

Insert parentheses so that the following expression simplifies to 28 . $$ 2 \cdot 5+3^{2} $$

For Exercises 107 through 110 , determine whether each statement is true or false. The sum of two positive numbers is always a positive number.

Write an example that shows that subtraction is not commutative.

Determine whether each is an expression or an equation. a. \(5 x+6\) b. \(2 a=7\) c. \(3 a+2=9\) d. \(4 x+3 y-8 z\) e. \(5^{2}-2(6-2)\)

For Exercises 107 through 110 , determine whether each statement is true or false. The sum of a positive number and a negative number is always a negative number.

Determine whether each is an expression or an equation. a. \(3 x^{2}-26\) b. \(3 x^{2}-26=1\) c. \(2 x-5=7 x-5\) d. \(9 y+x-8\) e. \(3^{2}-4(5-3)\)

For Exercises 107 through 110 , determine whether each statement is true or false. The sum of zero and a negative number is always a negative number.

In your own words, explain how to add two negative numbers.

Decide whether the given number is a solution of the given equation. \(-3 x-5=-20 ; 5\)

In your own words, explain how to add a positive number and a negative number.

Write any expression, using 3 or more numbers, that simplifies to -11.

Decide whether the given number is a solution of the given equation. \(\frac{x}{5}+2=-1 ; 15\)

Write any expression, using 4 or more numbers that simplifies to 7 .

Decide whether the given number is a solution of the given equation. \(\frac{x}{6}-3=5 ; 48\)

Decide whether the given number is a solution of the given equation. \(\frac{x-3}{7}=-2 ;-11\)

Decide whether the given number is a solution of the given equation. \(\frac{x+4}{5}=-6 ; \quad-30\)