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Arithmetics
Order of operations

Sometimes it's hard to know what to do first with a mathematical equation. The order of operations, sometimes called PEMDAS, is how we know what to operation to do first so that we always get the right answer. When adding, subtracting, multiplying, or dividing numbers, if we didn't use the order of operations we would get different answers for the same equation.

Remember the rules for order of operations:

1. First perform any calculations inside square brackets.
2. Next perform any calculations inside parentheses.
3. Next perform all multiplications and divisions, working from left to right.
4. Lastly, perform all additions and subtractions, working from left to right.

Simplify
4 · [ 9 · (8-6+4) -8 ] +2 · [ 24-2·(9+3-9) -3 ]

Solution:
4·[ 9·(8-6+4) -8 ] +2·[ 24-2·(9+3-9) -3 ]=
4·[9·6-8]+2·[24-2·3-3]=
4·[54-8]+2·[24-6-3]=
4·46+2·15=
184+30=214

The common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally".

 P Parentheses first E Exponents (ie Powers and Square Roots, etc.) MD Multiplication and Division (left-to-right) AS Addition and Subtraction (left-to-right)

Note: in the UK they say BODMAS (Brackets,Orders,Divide,Multiply,Add,Subtract), and in Canada they say BEDMAS (Brackets,Exponents,Divide,Multiply,Add,Subtract). It all means the same thing!

Simplify 8+8÷22-6

Solution:
8+8÷22-6 = 8+8÷4-6 = 8+2-6 = 10-6 = 4

Solve:

$8[7(3-6+4)-2]+5[7(5+6+1)+2]\;=\;$