Expert: Lynn Houston - 12/7/2011

Question
Hello:

How should this calculation be solved?

(1/7)/ 15 X 21 = ?

I get two answers. If 1/7 is divided by 15 the result is 1/105. If this is multiplied by 21, the result is 21/105 = 1/5.

However, if 15 and 21 are multiplied first, the result becomes (1/7)/315 = 1/2205.

Furthermore, if 15 and 21 are reversed as in (1/7)/ 21 X 15, the result is none of the above, 15/147.

Which calculation is correct and why?

Do the "orders of operations" apply to this calculation?

I thank you for your reply.

Answer
As you have it (1/7)/ 15 X 21, then 1/5 is the correct answer.  Remember PEMDAS, which stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction

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)

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)