Elementary arithmetic is the simplified portion of arithmetic that includes the operations of addition, subtraction, multiplication, and division. … Elementary arithmetic also includes fractions and negative numbers, which can be represented on a number line.

Below are some elementary mathematics problems that you can try at your own time. Tell me what you think about them, are they difficult? Which topics are a problem for you?

\begin{enumerate}

\item Simplify without using a calculator:
\begin{enumerate}
\item ${\left(\frac{5}{4^{-1}-9^{-1}}\right)^{\frac{1}{2}}}$
\item$(x^0)+5x^0-(0,25)^{-0,5}+8^{\frac{2}{3}}$
\item$s^{\frac{1}{2}}\div s^{\frac{1}{3}}$
\item$(64m^6)^\frac{2}{3}$
\item $\dfrac{12m^{\frac{7}{9}}}{8m^{-\frac{11}{9}}}$

\item $(x^3)^\frac{4}{3}$
\item $(s^2)^\frac{1}{2}$
\item $(m^5)^\frac{5}{3}$
\item $(-m^2)^\frac{4}{3}$
\item $(3y^\frac{4}{3})^4$
\end{enumerate}

\begin{itemize}

\item (a) $\left(-2{y}^{2}-4y+11\right) + \left(5y-12\right)$
\item (b) $\left(-11y+3\right)+ \left(-10{y}^{2}-7y-9\right)$
\item (c) $\left(4{y}^{2}+12y+10\right)+\left(-9{y}^{2}+8y+2\right)$
\item (d) $\left(7{y}^{2}-6y-8\right) – \left(-2y+2\right)$
\item (e) $\left(10{y}^{5}+3\right)-\left(-2{y}^{2}-11y+2\right)$
\item (f) $\left(-12y-3\right) + \left(12{y}^{2}-11y+3\right)$
\end{itemize}

\item Show that the decimal $3,21\dot{1}\dot{8}$ is a rational number.
\item Express $0,7\dot{8}$ as a fraction $\frac{a}{b}$ where $a,b\in \mathbb{Z}$
\item Round-off the following numbers to the indicated number of decimal places:\par
\begin{enumerate}
\item $\frac{120}{99}=1,212121212\dot{1}\dot{2}$ to 3 decimal places
\item $\pi =3,141592654…$ to 4 decimal places
\item $\sqrt{3}=1,7320508…$ to 4 decimal places
\item $2,78974526…$ to 3 decimal places
\end{enumerate}

\item Write the following irrational numbers to 3 decimal places and then write them as a rational number to get an approximation to the irrational number. For example, $\sqrt{3}=1,73205…$. To 3 decimal places, $\sqrt{3}=1,732$. $1,732=1\frac{732}{1000}=1\frac{183}{250}$. Therefore, $\sqrt{3}$ is approximately $1\frac{183}{250}$.

\begin{enumerate}
\item $3,141592654…$
\item $1,41421356…$
\item $2,71828182845904523536…$
\end{enumerate}

\item Simplify:
\begin{enumerate}
\item $2^{3x} \times 2^{4x}$
\item $\dfrac{12p^2t^5}{3pt^3}$
\item $(3x)^2$
\item $(3^4 5^2)^3$
\end{enumerate}

\item  Solve for the variable:
\begin{enumerate}
\item $2^{x+5} = 32$
\item $5^{2x+2} = \frac{1}{125}$
\item $64^{y+1} = 16^{2y+5}$
\item $3^{9x-2} = 27$
\item $81^{k+2} = 27^{k+4}$
\item $25^{(1-2x)}-5^4 = 0$
\item $27^x \times 9^{x-2} = 1$
\item $2^t + 2^{t+2} = 40$
\item $2 \times 5^{2-x} = 5+ 5^x$
\item $9^m + 3^{3-2m} = 28$

\end{enumerate}

\item  The growth of algae can be modelled by the function $f(t) = 2^t$. Find the value of $t$ such that $f(t)=128$.
\item  A type of bacteria has a very high exponential growth rate at $80\%$ every hour. If there are $10$ bacteria, determine how many there will be in five hours?

\end{enumerate}