Question

Evaluate the following expression: `4-7-:(3+1)-3-2*(5-9)+1` By how much does the value of the expression change if the parentheses are removed?

Answer 1

`8 1/4 + 18 1/3" "` = `26 (3 + 4)/12" "` = `26 7/12`
This is the change in the value of the expression.

Explanation:

The best way to approach calculations involving mixed operations, is to realise that there are "powerful" operations and "weak" operations.
The strongest operations are powers and roots ,
then come multiplication and division ;
the weakest are addition and subtraction.
They are therefore done in this order.
However, sometimes a weaker operation must be done first and that is indicated with parentheses, or brackets.

ALWAYS count the number of terms first!! (They are separated by the + and - signs).
There must be a final answer for each term, only then can they be added or subtracted - usually working from left to right, although this can be changed, using the commutative law, to make computation easier.

This is what is indicated by BODMAS, PEDMAS, etc.

In `color(green)(4) color(blue)(- 7 ÷ (3 + 1)) color(red)( - 3) color(turquoise)( - 2 xx (5 - 9)) color(orange)(+ 1)` there are 5 terms
`rArr color(green)(4) color(blue)(- 7/4) color(red)( - 3) color(turquoise) ( - 2xx(-4)) color(orange)( + 1)`

`rArrcolor(green)(4) color(turquoise) ( +8) color(orange)( + 1) color(red)( -3) color(blue)(- 1 3/4)`

`= 10 color(blue)(-1 3/4)`

= `8 1/4`

Without the parentheses, there are 7 terms:

`color(green)(4) color(blue)( - 7 ÷ 3) + 1 color(red)( - 3) color(turquoise)( - 2 xx 5) - 9 color(orange)( + 1)`
= `4 - 7/3 + 1 - 3 - 10 - 9 + 1`
= `4 + 1 +1 - 3 - 10 - 9 - 2 1/3`
= `6 - 24 1/3`

= `-18 1/3`

The difference between the two answers is
`8 1/4 - (-18 1/3)"` `rArr` `8 1/4 + 18 1/3`

= `26 (3 + 4)/12`

= `26 7/12`