\begin{testbox}
    \begin{questions}
        \question[6] Express each percentage as a fraction in its simplest form.
        \begin{parts}\begin{multicols}{2}
            \part \(18 \%\)
            \begin{solutionordottedlines}[1cm]
            $\frac{18}{100} = \frac{9}{50}$
            \end{solutionordottedlines}
            \part \(64 \%\)
            \begin{solutionordottedlines}[1cm]
            $\frac{64}{100} = \frac{16}{25}$
            \end{solutionordottedlines}
            \part \(2.6 \%\)
            \begin{solutionordottedlines}[1cm]
            $\frac{2.6}{100} = \frac{26}{1000} = \frac{13}{500}$
            \end{solutionordottedlines}
            \part \(8.5 \%\)
            \begin{solutionordottedlines}[1cm]
            $\frac{8.5}{100} = \frac{85}{1000} = \frac{17}{200}$
            \end{solutionordottedlines}
            \part \(37 \frac{1}{2} \%\)
            \begin{solutionordottedlines}[1cm]
            $37.5\% = \frac{37.5}{100} = \frac{375}{1000} = \frac{3}{8}$
            \end{solutionordottedlines}
            \part \(6 \frac{2}{3} \%\)
            \begin{solutionordottedlines}[1cm]
            $6\frac{2}{3}\% = \frac{20}{3} \times \frac{1}{100} = \frac{20}{300} = \frac{2}{30} = \frac{1}{15}$
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[6] Express each percentage as a decimal.
        \begin{parts}\begin{multicols}{2}
            \part \(8 \%\)
            \begin{solutionordottedlines}[1cm]
            $0.08$
            \end{solutionordottedlines}
            \part \(27 \%\)
            \begin{solutionordottedlines}[1cm]
            $0.27$
            \end{solutionordottedlines}
            \part \(9.6 \%\)
            \begin{solutionordottedlines}[1cm]
            $0.096$
            \end{solutionordottedlines}
            \part \(45.8 \%\)
            \begin{solutionordottedlines}[1cm]
            $0.458$
            \end{solutionordottedlines}
            \part \(12 \frac{1}{4} \%\)
            \begin{solutionordottedlines}[1cm]
            $12.25\% = 0.1225$
            \end{solutionordottedlines}
            \part \(38 \frac{1}{2} \%\)
            \begin{solutionordottedlines}[1cm]
            $38.5\% = 0.385$
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[6] Express each rational number as a percentage.
        \begin{parts}\begin{multicols}{2}
            \part \(\frac{2}{5}\)
            \begin{solutionordottedlines}[1cm]
            $\frac{2}{5} = 0.4 = 40\%$
            \end{solutionordottedlines}
            \part \(\frac{5}{8}\)
            \begin{solutionordottedlines}[1cm]
            $\frac{5}{8} = 0.625 = 62.5\%$
            \end{solutionordottedlines}
            \part 0.61
            \begin{solutionordottedlines}[1cm]
            $0.61 = 61\%$
            \end{solutionordottedlines}
            \part 0.02
            \begin{solutionordottedlines}[1cm]
            $0.02 = 2\%$
            \end{solutionordottedlines}
            \part \(\frac{4}{7}\)
            \begin{solutionordottedlines}[1cm]
            $\frac{4}{7} \approx 0.5714 = 57.14\%$
            \end{solutionordottedlines}
            \part \(\frac{5}{9}\)
            \begin{solutionordottedlines}[1cm]
            $\frac{5}{9} \approx 0.5556 = 55.56\%$
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[12] Complete the following table.
            \begin{center}
            \begin{tabular}{|c|c|c|c|}
            \hline
                & Percentage & Fraction & Decimal \\
                \hline
                a & 25\% & $\frac{1}{4}$ & 0.25 \\
                \hline
                b & 30\% & $\frac{3}{10}$ & 0.3 \\
                \hline
                c & 26\% & $\frac{13}{50}$ & 0.26 \\
                \hline
                d & 66.67\% & $\frac{2}{3}$ & 0.6667 \\
                \hline
                e & 8\% & $\frac{2}{25}$ & 0.08 \\
                \hline
                f & 7.5\% & $\frac{3}{40}$ & 0.075 \\
                \hline
            \end{tabular}
            \end{center}
        \question[4] Calculate:
        \begin{parts}
            \part \(8 \%\) of 120
            \begin{solutionordottedlines}[1cm]
            $120 \times 0.08 = 9.6$
            \end{solutionordottedlines}
            \part \(16 \%\) of 54
            \begin{solutionordottedlines}[1cm]
            $54 \times 0.16 = 8.64$
            \end{solutionordottedlines}
            \part \(85 \%\) of \(\$ 400\)
            \begin{solutionordottedlines}[1cm]
            $400 \times 0.85 = \$340$
            \end{solutionordottedlines}
            \part \(9 \frac{1}{2} \%\) of \(\$ 6000\)
            \begin{solutionordottedlines}[1cm]
            $6000 \times 0.095 = \$570$
            \end{solutionordottedlines}
        \end{parts}
        \question[2] There are 650 students at a high school, \(54 \%\) of whom are boys. How many boys are at the school?
            \begin{solutionordottedlines}[1in]
            $650 \times 0.54 = 351$
            \end{solutionordottedlines}
        \question[2] Netball is played by \(6 \%\) of Australians. If the population of Australia is 22500000 , how many Australians play netball?
            \begin{solutionordottedlines}[1in]
            $22500000 \times 0.06 = 1350000$
            \end{solutionordottedlines}
        \question[2] In a class of 25 students, 8 travel to school by train. What percentage of the class travel to school by train?
            \begin{solutionordottedlines}[1in]
            $\frac{8}{25} = 0.32 = 32\%$
            \end{solutionordottedlines}
        \question[2] In a survey of 1200 adults, it was discovered that 114 of them were unemployed. What percentage of the adults surveyed were unemployed?
            \begin{solutionordottedlines}[1in]
            $\frac{114}{1200} = 0.095 = 9.5\%$
            \end{solutionordottedlines}
        \question[4] Find the new value if:
        \begin{parts}\begin{multicols}{2}
            \part 80 is increased by \(40 \%\)
            \begin{solutionordottedlines}[1cm]
            $80 \times 1.40 = 112$
            \end{solutionordottedlines}
            \part 150 is increased by \(6 \%\)
            \begin{solutionordottedlines}[1cm]
            $150 \times 1.06 = 159$
            \end{solutionordottedlines}
            \part 240 is decreased by \(12 \%\)
            \begin{solutionordottedlines}[1cm]
            $240 \times 0.88 = 211.2$
            \end{solutionordottedlines}
            \part 160 is decreased by \(4 \%\)
            \begin{solutionordottedlines}[1cm]
            $160 \times 0.96 = 153.6$
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \question[2] During a sale, the price of a sofa bed is reduced by \(20 \%\). If the original price of the bed was \(\$ 650\), what is its sale price?
            \begin{solutionordottedlines}[1in]
            $650 \times 0.80 = \$520$
            \end{solutionordottedlines}
        \question[2] A salesperson is given a salary increase of \(4 \%\). If her existing weekly salary is \(\$ 640\), what will her new weekly salary be?
            \begin{solutionordottedlines}[1in]
            $640 \times 1.04 = \$665.60$
            \end{solutionordottedlines}
        \question[2] Joe's Electrical Store is having an \(8 \%\) discount sale. The sale price of some items is given below. Calculate the price of the items before they were reduced.
            \begin{solutionordottedlines}[1in]
            \end{solutionordottedlines}
        \begin{parts}
            \part Heater \(\$ 276\)
            \begin{solutionordottedlines}[1cm]
            $276 \div 0.92 = \$300$
            \end{solutionordottedlines}
            \part Vacuum cleaner \(\$ 138\)
            \begin{solutionordottedlines}[1cm]
            $138 \div 0.92 = \$150$
            \end{solutionordottedlines}
            \part Dishwasher \(\$ 690\)
            \begin{solutionordottedlines}[1cm]
            $690 \div 0.92 = \$750$
            \end{solutionordottedlines}
            \part Microwave \(\$ 132.80\)
            \begin{solutionordottedlines}[1cm]
            $132.80 \div 0.92 = \$144.35$
            \end{solutionordottedlines}
        \end{parts}
        \question[2] The enrolment of a school increased from 680 to 740 . Calculate the percentage increase, correct to 2 decimal places.
            \begin{solutionordottedlines}[1in]
            $\frac{740 - 680}{680} \times 100 \approx 8.82\%$
            \end{solutionordottedlines}
        \question[2] During a sale the price of a suit is reduced from \(\$ 420\) to \(\$ 370\). Calculate the percentage discount, correct to 1 decimal place.
            \begin{solutionordottedlines}[1in]
            $\frac{420 - 370}{420} \times 100 \approx 11.9\%$
            \end{solutionordottedlines}
        \question[4] What single percentage change, correct to 2 decimal places, is equivalent to each of these multiple changes?
        \begin{parts}
            \part A \(6 \%\) increase followed by a \(12 \%\) increase
            \begin{solutionordottedlines}[1cm]
            $1.06 \times 1.12 = 1.1872 \approx 18.72\%$ increase
            \end{solutionordottedlines}
            \part A \(10 \%\) increase followed by a \(10 \%\) decrease
            \begin{solutionordottedlines}[1cm]
            $1.10 \times 0.90 = 0.99 = 1\%$ decrease
            \end{solutionordottedlines}
            \part A \(16 \%\) decrease followed by a \(8 \%\) decrease
            \begin{solutionordottedlines}[1cm]
            $0.84 \times 0.92 = 0.7728 \approx 22.72\%$ decrease
            \end{solutionordottedlines}
            \part A \(12 \%\) decrease followed by a \(14 \%\) increase
            \begin{solutionordottedlines}[1cm]
            $0.88 \times 1.14 = 1.0032 \approx 0.32\%$ increase
            \end{solutionordottedlines}
        \end{parts}
        \question[2] Over the course of a year an employee is given successive salary increases of \(4 \%, 6 \%\) and 5\%.
            \begin{solutionordottedlines}[1in]
            \end{solutionordottedlines}
        \begin{parts}
            \part If the employee's original monthly salary was \(\$ 2600\), what is the employee's salary after the three increases?
            \begin{solutionordottedlines}[2cm]
            $2600 \times 1.04 \times 1.06 \times 1.05 = \$3038.28$
            \end{solutionordottedlines}
            \part What single percentage change is equivalent to the three successive salary increases?
            \begin{solutionordottedlines}[2cm]
            $1.04 \times 1.06 \times 1.05 = 1.1688 \approx 16.88\%$ increase
            \end{solutionordottedlines}
        \end{parts}
        \question[2] To obtain a bonus, a salesperson's sales must increase by \(20 \%\) in a two-month period. If the salesperson's sales increase by \(8 \%\) in the first month, by what percentage must they increase in the second month to ensure the bonus is obtained?
            \begin{solutionordottedlines}[2cm]
            Let $x$ be the required percentage increase for the second month.
            $1.08 \times (1 + \frac{x}{100}) = 1.20$
            $1 + \frac{x}{100} = \frac{1.20}{1.08}$
            $\frac{x}{100} = \frac{1.20}{1.08} - 1$
            $x = (1.1111 - 1) \times 100$
            $x \approx 11.11\%$
            \end{solutionordottedlines}
        \question[2] Mia invests \(\$ 6000\) in the bank. How much will she have in her account after three years if the bank pays:
        \begin{parts}
            \part \(8 \%\) simple interest p.a.
            \begin{solutionordottedlines}[2cm]
            $6000 + (6000 \times 0.08 \times 3) = 6000 + 1440 = \$7440$
            \end{solutionordottedlines}
            \part \(4 \%\) compound interest p.a.
            \begin{solutionordottedlines}[2cm]
            $6000 \times (1 + 0.04)^3 \approx 6000 \times 1.124864 = \$6749.18$
            \end{solutionordottedlines}
        \end{parts}
        \question[3] The value of a new car depreciates at a compound rate of \(6 \%\) each year. If the car has an initial value of \(\$ 19960\), calculate its value after:
        \begin{parts}
            \part one year
            \begin{solutionordottedlines}[2cm]
            $19960 \times (1 - 0.06) = 19960 \times 0.94 = \$18762.40$
            \end{solutionordottedlines}
            \part five years
            \begin{solutionordottedlines}[2cm]
            $19960 \times (1 - 0.06)^5 \approx 19960 \times 0.747258 = \$14920.47$
            \end{solutionordottedlines}
            \part 10 years
            \begin{solutionordottedlines}[2cm]
            $19960 \times (1 - 0.06)^{10} \approx 19960 \times 0.558395 = \$11145.89$
            \end{solutionordottedlines}
        \end{parts}
    \end{questions}
\end{testbox}
