Chapter 1

\(9^{2} \div 3-12(4-6)\)

Problem: Simplify: \(4-(x+9)\) Incorrect Answer: \(4-(x+9)\) $$ \begin{aligned} &=4-x+9 \\ &=-x+13 \end{aligned} $$

\(8^{2} \div 4-12(2-7)\)

Problem: The diameter of a circle is \(10 \mathrm{in}\). Using \(\pi \approx 3.14\), find the area of the circle. Incorrect Answer: \(A=\pi r^{2}\) $$ \begin{aligned} A &=(3.14)(10 \text { in. })^{2} \\ A &=(3.14)\left(100 \mathrm{in}^{2}\right) \\ A &=314 \mathrm{in}^{2} \end{aligned} $$

The shape of a building lot is a trapezoid with bases that measure \(150 \mathrm{ft}\) and \(400 \mathrm{ft}\). The height is \(220 \mathrm{ft}\). Find the area of the lot.

Problem: Simplify: \(8(4 x-1)-3(2 x-5)\) $$ \text { Incorrect Answer: } \begin{aligned} 8 &(4 x-1)-3(2 x-5) \\ &=8(4 x)+8(-1)-3(2 x)-3(5) \\ &=32 x-8-6 x-15 \\ &=26 x-23 \end{aligned} $$

The shape of a table top is a trapezoid with bases that measure \(25 \mathrm{in}\). and \(60 \mathrm{in}\). The height is \(30 \mathrm{in}\). Find the area of this table.

Problem: Simplify: \(12 x+15 y+3 x+2 y\) Incorrect Answer: \(12 x+15 y+3 x+2 y\) $$ \begin{aligned} &=15 x+17 y \\ &=32 x y \end{aligned} $$

Problem: Evaluate: \(\sqrt[3]{-216}\) Incorrect Answer: \(\sqrt[3]{-216}\) is not a real number.

A quilter is buying fabric that is 44 in. wide to make a back for a rectangular quilt that is 102 in. wide and 120 in. long. The quilter needs to buy three strips of fabric that are as wide as the quilt plus two additional inches of fabric on each end of the strip. Find the amount of fabric in yards that the quilter should buy. Round \(u p\) to the nearest tenth.

Describe the order of operations.

\(5^{3}+3 \cdot 8 \div(-4-2)\)

Problem: Find the volume of a cylinder with a diameter of 14 in. and a height of \(2 \mathrm{ft}\). Write the answer in cubic inches. Use \(\pi \approx 3.14\). Incorrect Answer: \(V=\pi r^{2} h\) $$ \begin{aligned} &V=(3.14)(7 \text { in. })^{2}(2 \mathrm{ft}) \\ &V=(3.14)\left(49 \text { in. }^{2}\right)(2 \mathrm{ft}) \\ &V=307.72 \text { in. }^{3} \end{aligned} $$

Roofing shingles are sold by the "square." A square can cover an area of roof that is \(10 \mathrm{ft}\) long and \(10 \mathrm{ft}\) wide. The area of a roof is \(3450 \mathrm{ft}^{2}\). Find the number of squares of roofing shingles needed to cover this roof. Round up to the nearest whole number.

Explain the difference between a rational number and an irrational number.

\(4^{3}+4 \cdot 6 \div(-4-2)\)

Problem: Find the simple interest earned on \(\$ 300\) invested for 5 years at an annual simple interest rate of \(4.5 \%\). Incorrect Answer: \(I=P R T\) $$ \begin{aligned} &I=(\$ 300)\left(\frac{4.5}{1 \text { year }}\right)(5 \text { years }) \\ &I=\$ 6750 \end{aligned} $$

\(\frac{3^{2}-5 \cdot 9}{-6^{2}}\)

\(\frac{6 \cdot 8-8^{2}}{-4^{2}}\)

Problem: The length of a rectangle is \(3 \mathrm{~cm}\). Its width is \(8 \mathrm{~cm}\). Find its area. $$ \text { Incorrect Answer: } \begin{aligned} A &=L W \\ A &=3 \cdot 8 \\ A &=24 \end{aligned} $$

\(\frac{4\left(5^{2}-6 \cdot 4\right)}{3 \cdot 4-6 \cdot 2}\)

\(\frac{3\left(4^{2}-5 \cdot 2\right)}{4 \cdot 8-2 \cdot 16}\)

\(\frac{2}{3}(6 x-8)-\frac{7}{10} x+4\)

\(\frac{1}{3} \cdot \frac{1}{8} \div \frac{5}{6}\)

\(\frac{2}{15} h-\frac{5}{8} h+\frac{4}{5} k-\frac{1}{12} k\)

\(\frac{1}{5} \cdot \frac{1}{12} \div \frac{5}{6}\)

\(-6(3 z-7)-(2 z+1)\)

\(\frac{1}{2}(12-7)-\frac{1}{4}(17-14)\)

\(-8(9 x-5)-(4 x+1)\)

\(\frac{1}{2}(11-4)-\frac{3}{4}(15-12)\)

\(\frac{2}{9}+\frac{2}{9} \div\left(-\frac{1}{5}\right)\)

\(-\frac{2}{7}+\frac{2}{7} \div\left(-\frac{1}{3}\right)^{2}\)

\(-\frac{4}{9}+\frac{2}{9} \div\left(-\frac{1}{5}\right)^{2}\)

\(\left(9-3^{2}\right) \div 18\)

\(\left(25-5^{2}\right) \div 10\)

\([10-3(2+7)+20]^{2}\)

\([18-3(4+9)+25]^{2}\)

\(2[21 \div 3(7-4)]\)

\(2[15 \div 3(5-1)]\)

Write your own example of an expression that includes multiplication, division, and subtraction. When this expression is evaluated, it equals 5 .

Write your own example of an expression that includes multiplication, division, and addition. When this expression is evaluated, it equals 6 .

Write your own example of an expression that includes one set of parentheses and an exponent. When this expression is evaluated, it equals 4 .

\(3\left(\frac{1}{5}-\frac{2}{3}\right)-4^{2}\)

\(4+20-(7+12 \div(2+1))\)

\((9-1)^{2}-(4+3)^{2}\)

\(\frac{18-5+2}{1-4}\)

Problem: Evaluate: \(100-25 \div 5\) Incorrect Answer: \(100-25 \div 5\) $$ \begin{aligned} &=75 \div 5 \\ &=15 \end{aligned} $$

Problem: Evaluate: \(4+(7-1)^{2}\) Incorrect Answer: \(4+(7-1)^{2}\) $$ \begin{aligned} &=4+6^{2} \\ &=4+12 \\ &=16 \end{aligned} $$

Problem: Evaluate: \(-6-(-2)(5)\) $$ \begin{aligned} \text { Incorrect Answer: } &-6-(-2)(5) \\ &=-6-10 \\ &=-16 \end{aligned} $$

Problem: Evaluate: \(-3^{2}+8 \div(-2)\) Incorrect Answer: \(-3^{2}+8 \div(-2)\) $$ \begin{aligned} &=9+8 \div(-2) \\ &=9+(-4) \\ &=5 \end{aligned} $$