Question

Put on set of parenthesis to make this equation correct
8-2^2/9+11

Answer 1

To make the equation \( 8 - 2^2 / 9 + 11 \) correct by adding a set of parentheses, we can try the following:

1. First, let's simplify the equation without parentheses:
\[
8 - \frac{2^2}{9} + 11
\]
This simplifies to:
\[
8 - \frac{4}{9} + 11
\]
Which becomes:
\[
8 + 11 - \frac{4}{9} = 19 - \frac{4}{9} = \frac{171}{9} - \frac{4}{9} = \frac{167}{9}
\]

Now, let's add parentheses to change the order of operations. One way to do this is to group \(2^2\) and the entire division and addition as follows:
\[
8 - \left(\frac{2^2}{9 + 11}\right)
\]
This simplifies to:
\[
8 - \left(\frac{4}{20}\right) \equiv 8 - 0.2 = 7.8
\]

To achieve some common value such as 19, we can try out various placements of parentheses.

Another way could be:
\[
(8 - 2^2) / 9 + 11
\]
This gives:
\[
(8-4) / 9 + 11 = 4 / 9 + 11
\]

The best approach to obtain integer values is thus not unique. However, a combination like:
\[
8 - (2^2 / (9 + 11))
\]
Finally converging to integer results rather than fractions should be re-evaluated till desired value achieved or known equivalences sought.

The overall conclusion is that the positioning of parentheses will depend on what final value you aim for.