logo for solving-math-problems.com
leftimage for solving-math-problems.com

PEMDAS - Evaluate Ambiguous Expression: 48 ÷ 2 (9+3)











































using PEMDAS, order of operations, to evaluate an ambiguous expression

is the answer 2 to this equation answer to this question 48 / 2 (9+3) =

Comments for PEMDAS - Evaluate Ambiguous Expression: 48 ÷ 2 (9+3)

Click here to add your own comments

Feb 04, 2013
Ambiguous Expression
by: Staff


Answer

48 / 2 (9+3) = ?

The meaning of the expression has been widely debated since it appeared on an internet forum called HotPursuit (http://www.hotpursuit.cc/forum/) several years ago.

The expression is unclear. It is ambiguous.

It is a good EXAMPLE of HOW NOT TO WRITE AN EXPRESSION.

What does it mean?

          48
-------- = 2
2 (9+3)

or

48
------(9+3) = 288
2


The answer is: When the meaning is unclear, read from left to right.

Reading the expression from left to right will eliminate the problems between PEMDAS, BEDMAS (Canadian system), BIDMAS (UK), or BODMAS (UK) as the order of operations.
Reversing the MD in PEMDAS for DM in Canadian and British systems will not change the answer.

When the expression is carefully read and evaluated from left to right, the results of all systems are the same.



How to calculate a value for the expression 48 / 2 (9+3)

48 / 2 (9+3) = ?

To simplify this expression:

Use the PEMDAS order of operations.

PEMDAS order tells you what to do first, second, . . . etc.

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction




Step 1: evaluate PARENTHESES

PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

48 / 2 (9 + 3)

There is one parentheses to evaluate: (9 + 3)

(9 + 3)

= 9 + 3

= 12


After evaluating the expression inside the parentheses, the expression looks like this:

48 / 2 (12)



Step 2: evaluate EXPONENTS


PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

There are no exponents to evaluate.


Step 3: Now What? The entire PEMDAS system seems to break down.

Since the expression is unclear, read from left to right.

When the problem is read from left to right, the first operation encountered is division:

48 / 2

= 48 / 2

= 24

After completing the division, the expression looks like this:

24 (12)

When the problem is read from left to right, the next operation encountered is multiplication:

24 (12)

= 24 × 12

= 288

Final Answer:

288



-------------------------------------------

Feb 04, 2013
Ambiguous Expression
by: Staff


-------------------------------------------



Part II


Verify that the answer really is “288” using A "Formula" Calculator.


The correct answer is based upon PEMDAS . . . PAMDAS applied mechanically.


A Formula Calculator (Smart Calculator) automatically takes PEMDAS order into account.

The person using the calculator does not need to be concerned about which numbers to evaluate 1st, 2nd, 3rd, etc.

Type the entire expression into the “formula” calculator, just as it appears:

48 / 2 (9 + 3), or 48 / 2 * (9 + 3)


Don’t change anything.

You can download free formula calculators here:



Free Formula Calculators

Download or Use "SMART" Calculators on-line for Free


http://calcute.com/


http://www.fox-toolkit.org/download.html


http://www.google.com/search?hl=en&q=2%2B2%3D&btnG=Search


http://www.alemoi.com/math/








Thanks for writing.

Staff
www.solving-math-problems.com

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com