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?

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.

Without the parentheses, there are 7 terms:

To evaluate the given expression:

4 - 7 ÷ (3 + 1) - 3 - 2 * (5 - 9) + 1

We follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we evaluate expressions within parentheses: 5 - 9 = -4 3 + 1 = 4

Next, we perform multiplication and division: 7 ÷ 4 = 1.75 2 * (-4) = -8

Then, we perform addition and subtraction: 4 - 1.75 - 3 - (-8) + 1 = 4 - 1.75 - 3 + 8 + 1 = 4 - 1.75 - 3 + 8 + 1 = 7.25

So, the value of the expression is 7.25.

If the parentheses are removed, the expression becomes:

4 - 7 ÷ 3 + 1 - 3 - 2 * 5 - 9 + 1

Following the order of operations, we evaluate this expression:

4 - 7 ÷ 3 + 1 - 3 - 2 * 5 - 9 + 1 = 4 - 2.333 + 1 - 3 - 10 - 9 + 1 = 4 - 2.333 + 1 - 3 - 10 - 9 + 1 = -18.333

So, the value of the expression without parentheses is -18.333.

The difference in value between the two expressions is:

7.25 - (-18.333) = 25.583

Therefore, the value of the expression changes by 25.583 when the parentheses are removed.