Basic(Elementary) Mathematics

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Oders of Operations

There are a lot of post on social media discussing about this topic, but the rule is just PEMDAS from left to right.

  1. Parenthesis - Perform operations inside the parenthesis.
  2. Exponents - Perform exponents if there are exponents, do not create exponents for the sake of having an operation "E" . If there are exponents given then use the operation, if not this does not mean we need to rewrite numbers interms of exponents so that we can use "exponent".
    1. Example: 100 x 10 x 5 ÷ 3: We do not write 103 x 5 ÷ 3, so that we could use E from PEMDAS. Since there is no exponent on the original problem then we just proceed from multiplication to division.
  3. Multiplication or Division - Perform multiplication or division what ever comes first from left to right.
  4. Addition or Subtraction - Perform addition or subtraction what ever comes first from left to right.
    5. Note: In a single digit 2(3), this means 2 x 3. The parenthesis may be changed to multiplication sign.

Here is a PEMDAS flow chart

Folow Chart of PEMDAS

Examples:

  1. Here is an example similar to a familar problem on facebook: 25÷5(2 + 3 ). Is the answer 25 or 1? Lets analyze.
    1. Inside the parenthesis: 25÷5(5)
    2. 25÷5x5: Since () denotes multiplication
    3. 5x5: Division from left to right
    4. 25: Answer
  2. Some of the comments said there that, there should be an "E" (exponent) before division or multiplication, here is the argument.
    1. Inside the parenthesis: 25÷5(5)
    2. 25÷5x5: Since () denotes multiplication
    3. 25÷52: Since 5x5 = 52. Yeah it is true that 5x5 = 52, but under the rule it did not say rewrite - it is perform, so this step is wrong. We should perform what is in there.
    4. 25÷25: Division from left to right
    5. 1: Answer