Question

To complete this component you will need to insert parentheses in Expression 2 to change the order of operations so the expression will have a value of 19. 5+4*2+6-2*2-1

Answer 1

Given:

The expression is
`5+4* 2+6-2* 2-1`.

To find:

The position of parentheses inserted in the expression to get the value 19

Explanation:

We have,

`5+4* 2+6-2* 2-1`

Now,

`(5+4)* 2+6-2* 2-1=9* 2+6-4-1`

`(5+4)* 2+6-2* 2-1=18+6-5`

`(5+4)* 2+6-2* 2-1=18+1`

`(5+4)* 2+6-2* 2-1=19`

There are more ways to apply the parenthesis, but we do not get 19.

`5+4*\left(2+6\right)-2*2-1=32\\eq 19`

`5+4*2+\left(6-2\right)*2-1=20\\eq 19`

`5+4*2+6-2*\left(2-1\right)=17\\eq 19`

And many more possibilities.

Therefore, the expression after inserting the parentheses is
`(5+4)* 2+6-2* 2-1`.