# Using exactly four 3's and any math symbol, try to write an equivilent expression for each whole...

## Question:

Using exactly four 3's and any math symbol, try to write an equivilent expression for each whole number from 1 through 10.

Example: {eq}1 = \frac {\frac {3*3}{3}}{3} {/eq}.

## Forming an Expression for the Whole Number:

We need to find the arithmetic expression by using the arithmetic operators such as addition, subtraction, multiplication and division. And the number that we are using to find the expression should contain four {eq}3's. {/eq}

The expression for {eq}1 {/eq} can be written as,

\begin{align} 1= \frac{\left(3+3\right)-3}{3} \end{align}

The expression for {eq}2: {/eq}

\begin{align} 2= \frac{\left(3\cdot 3\right)-3}{3} \end{align}

The expression for {eq}3: {/eq}

\begin{align} 3= 3\cdot 3-\left(3+3\right) \end{align}

There is impossible to get the expression for {eq}4 {/eq} using the four {eq}3's. {/eq}

Since the expression for {eq}5: {/eq} can be,

\begin{align} 5=3+3-\frac{3}{3} \end{align}

And the expression for getting {eq}6: {/eq}

\begin{align} 6=3+3-\left(3-3\right) \end{align}

Expression for getting {eq}7: {/eq}

\begin{align} 7=3+3+\frac{3}{3} \end{align}

And the expression for {eq}8: {/eq}

\begin{align} 8=3\cdot 3-\frac{3}{3} \end{align}

The expression for getting {eq}9: {/eq}

\begin{align} 9=3\cdot 3-\left(3-3\right) \end{align}

And finally the expression for {eq}10: {/eq}

\begin{align} 10=3\cdot 3+\left(\frac{3}{3}\right). \end{align} 