The Simplifier

Example Three

3. Solve:
{1 – [1 – 1 x (1 + 1) – 1 ] of 1} ÷ 1 + 1

This has nested brackets (i.e. bracket inside another bracket and we must start from the innermost bracket).

Starting from innermost bracket:
{1 – [1 – 1 x (1 + 1) –1] of 1} ÷ 1 + 1

= {1 – [1 – 1 x 1 – 1] of 1} ÷ 1 + 1

Apply the Precedence Rule also in the Innermost Bracket:
 {1 – [1 – 1 x 1 – 1] of 1} ÷ 1 + 1

= {1 – [1 – 1 – 1] of 1} ÷ 1 + 1

Applying Precedent rule from left to right inside the bracket we have:
{1 – [1 – 1 – 1] of 1} ÷ 1 + 1

= {1 – [0 – 1] of 1} ÷ 1 + 1

Furthermore we have:
{1 – [0 – 1] of 1} ÷ 1 + 1

= {1 – [–1] of 1} ÷ 1 + 1

Next is to consider the of in the Innermost Bracket (if it exists):
{1 – (–1) of 1} ÷ 1 + 1

= {1 – (–1)} ÷ 1 + 1

Notice that we do not write two mathematical operators together without a bracket to separate them: e.g. instead of 1 – – 1 we write 1 – ( - 1).

Next Step finalize the operations in brackets to open up the expression:
{1 – (–1)} ÷ 1 + 1

=  2 ÷ 1 + 1

(note: - x - = - (-) = + e.g. -1 x (-1) = +1 or just 1)

Next Consider the Division first before Addition:
  2 ÷ 1 + 1 = 2 + 1 = 3  (note: 2/1 = 2 ÷ 1 = 2)

PS: Note the following:
1. Expression is not the same as equation:
Expression has no equality sign e.g. A ± B
Equation has an equality sign e.g. A = B
2. Any number written without a negative or positive in front is positive e.g. 2 is same as +2.

Keynote
To understand the mathematical process(es) you must learn to always make attempts. Don't read mathematics rather study and solve mathematics. Get a book for practice (solving problems).

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