Chapter 1.2, Problem 54WE

To determine

To calculate:

The expressions using the number $2$ four times, to get the values $0,1,2,3,4,5and6$ respectively.

Answer to Problem 54WE

The expressions using the number $2$ four times, to get the values $0,1,2,3,4,5and6$ respectively are:

  $\left(2-2\right)+\left(2-2\right)$

  $\left(2+2\right)÷\left(2+2\right)$

  $\left(2÷2\right)+\left(2÷2\right)$

  $2+2-\left(2÷2\right)$

  $\left[\left(2+2\right)+2\right]-2$

  $\left[\left(2+2\right)2\right]-2$

Explanation of Solution

Given information:

Use the number $2$ four times.

The expressions using the number $2$ four times, to get the values $0,1,2,3,4,5and6$ respectively:

To get value $0$ ,

  $2-2+2-2$

After grouping, the required value is $0$ :

  $\begin{array}{l}\left(2-2\right)+\left(2-2\right)\\ 0+0\\ 0\end{array}$

From the above calculation, the value is similar to the required value of the equation as $0$ .

Therefore, the expression having value $0$ using the number $2$ four times is:

  $\left(2-2\right)+\left(2-2\right)$

To get value $1$ ,

  $2+2÷2+2$

After grouping, the required value is $1$ :

  $\begin{array}{l}\left(2-2\right)+\left(2-2\right)\\ 0+0\\ 0\end{array}$

From the above calculation, the value is similar to the required value of the equation as $1$ .

Therefore, the expression having value $1$ using the number $2$ four times is:

  $\left(2+2\right)÷\left(2+2\right)$

To get value $2$ ,

  $2÷2+2÷2$

After grouping, the required value is $2$ :

  $\begin{array}{l}\left(2÷2\right)+\left(2÷2\right)\\ 1+1\\ 2\end{array}$

From the above calculation, the value is similar to the required value of the equation as $2$ .

Therefore, the expression having value $2$ using the number $2$ four times is:

  $\left(2÷2\right)+\left(2÷2\right)$

To get value $3$ ,

  $2+2-2÷2$

After grouping, the required value is $3$ :

  $\begin{array}{l}2+2-\left(2÷2\right)\\ 4-1\\ 3\end{array}$

From the above calculation, the value is similar to the required value of the equation as $3$ .

Therefore, the expression having value $3$ using the number $2$ four times is:

  $2+2-\left(2÷2\right)$

To get value $4$ ,

  $2+2+2-2$

After grouping, the required value is $4$ :

  $\begin{array}{l}\left[\left(2+2\right)+2\right]-2\\ \left[4+2\right]-2\\ 6-2\\ 4\end{array}$

From the above calculation, the value is similar to the required value of the equation as $4$ .

Therefore, the expression having value $4$ using the number $2$ four times is:

  $\left[\left(2+2\right)+2\right]-2$

To get value $5$ ,

  $2+2+2÷2$

After grouping, the required value is $5$ :

  $\begin{array}{l}\left(2+2\right)+\left(2÷2\right)\\ \left[4\right]+1\\ 5\end{array}$

From the above calculation, the value is similar to the required value of the equation as $5$ .

Therefore, the expression having value $5$ using the number $2$ four times is:

  $\left(2+2\right)+\left(2÷2\right)$

To get value $6$ ,

  $2+2\times 2-2$

After grouping, the required value is $6$ :

  $\begin{array}{l}\left[\left(2+2\right)2\right]-2\\ \left[4\times 2\right]-2\\ 8-2\\ 6\end{array}$

From the above calculation, the value is similar to the required value of the equation as $6$ .

Therefore, the expression having value $6$ using the number $2$ four times is:

  $\left[\left(2+2\right)2\right]-2$