Our answers are correct, ND....

The calculator confirms it......

5(6 / 22 * 3 - 1)

$${\mathtt{5}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{6}}}{{\mathtt{22}}}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,-\,}}{\mathtt{1}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{10}}}{{\mathtt{11}}}} = -{\mathtt{0.909\: \!090\: \!909\: \!090\: \!909\: \!1}}$$

And besides, two great minds like ours can never be mistaken............LOL!!!!

5[6 ÷ 22 · 3 - 1]

=5[6 ÷ 66 - 1]

=5[11 - 1]

=5 · 10

=50

Correction:

5[6 ÷ 22 · 3 - 1]

=5[2 ÷ 22 - 1]

=5[1/11 - 1]

=5/11 - 5

=-50/11

5[6 ÷ 22 · 3 - 1]    Remember that we perform any multiplications/divisions as we encounter them from left to right....so.....working inside the brackets first, we have

5[ (6/22)*(3) -1] =

5[(18/22) - 1] =

5[9/11 - 1] =

5[9/11 - 11/11] =

5 [-2/11] =

-10/11

We got some different answers here so I'll solve it myself and hopefully we'll get a two of the same answer.

5[6 ÷ 22 · 3 - 1]            ---Write this as a fraction

5[6/22 · 3 - 1]              ---Simplify the fraction

5[3/11 · 3 - 1]               ---Multiply 3/11 times 3

5[9/11 - 1]                     ---Rewrite as two fractions

5[9/11- 11/11]              ---Subtract

5[-2/11]                    ---Multiply out

-10/11

CPhill and I both got this answers, so it should be right.