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Order of Calculations

by Ben











































Use PEMDAS to compute the answer to the following expression.

30÷2(2+3)÷5=?

Is the answer 15 or 0.6?

This problem illustrates how important it is to include parentheses to clarify the order of operations.

Comments for Order of Calculations

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Apr 20, 2011
Order of Calculations
by: Staff

The question:

by Ben

30÷2(2+3)÷5=?
Is the answer 15 or 0.6?


The answer:

The answer is 15.


Read the expression from left to right


30÷2(2+3)÷5=?

(30 ÷ 2) * (2 + 3) ÷ 5 = ?

Left to right: do this first

(30 ÷ 2) = 15

Left to right: do this second

(2 + 3) = 5

Left to right: do this third

15 *5 = 75

Left to right: do this fourth

75/5 = 15


Using parentheses

[(30 ÷ 2) * (2 + 3)] ÷ 5 = ?

[(15) * (2 + 3)] ÷ 5 = ?

[(15) * (5)] ÷ 5 = ?

(75) ÷ 5 = ?

75 ÷ 5 = 15


Or (the answer will be the same)

30÷2(2+3)÷5=?

Left to right

(30 ÷ 2) * (2 + 3) ÷ 5 = ?

(30 ÷ 2) * [(2 + 3) ÷ 5] = ?

(30 ÷ 2) * [(5) ÷ 5] = ?

(30 ÷ 2) * (5 ÷ 5) = ?

(15) * (5 ÷ 5) = ?

(15) * (1) = ?

(15) * (1) = 15


This problem illustrates how important it is to include parentheses to clarify the order of operations.

[(30 ÷ 2) * (2 + 3)] ÷ 5 = ?

Instead of

30÷2(2+3)÷5=?



Thanks for writing.


Staff
www.solving-math-problems.com



Apr 20, 2011
Still a little confused
by: Ben

Many thanks for your answer.

30÷2(2+3)÷5=15

What would your comment be if anyone argues that:
2(2+3) should be calculated first before the rest of the calculations from left to right?

As in:

30 ÷ 2(2+3) ÷ 5 = ?
30 ÷ (4+6)÷ 5 = ?
30 ÷ 10 ÷ 5 = 0.6

Any difference in the answer by the way the mathematical question is expressed as below?
30÷2(2+3)÷5=0.6
30÷2x(2+3)÷5=15



Apr 20, 2011
Order of Calculations
by: Staff

Hi Ben,

2(2+3) cannot be calculated first because you MUST read from left to right.

However, (2+3) should be calculated first because that is the PEMDAS order.

Think about the PEMDAS order (left to right) as a set of rules we all agree upon. The rules are arbitrary. The point is that we all agree on the same rules so we can communicate.

As an example of how communication works, suppose you give me directions to your home.

You might say:

Start at the intersection of Street A and Street B.

Go south 3 blocks, then turn right for exactly 1/2 block. I live on your right. The address is: xxxxx.

My opinion regarding your directions does not matter. I cannot put my own spin on your directions without getting lost.

I will only arrive at your home if I understand WHAT YOU MEAN when you say “left” and “right”.

If I assign a different meaning to the words “left” and “right” than you assign, I will not find your home.

If we wanted to, we could both agree that the words “left” and “right” had the opposite meaning from what is generally accepted.

That would be OK since both of us would assign the same meaning to the directions you give.

You would know that I would go the opposite direction from the normal direction associated with “left” and “right”.

You could change your instructions so that everything was reversed.

That is exactly what is happening with PEMDAS order (left to right). The rules are arbitrary. There is nothing special about them.

However, mathematicians agree that PEMDAS order (left to right) will be followed so we can understand one another.

When a mathematician writes an expression for someone else to read, he or she will deliberately write so that the expression follows the PEMDAS order (left to right).

This will be done because the writer knows that whoever reads the expression or equation will read it in PEMDAS order (left to right).


Thanks for submitting your comment. You can be sure there are several hundred other people who have the same question, but didn’t say anything.


Staff
www.solving-math-problems.com


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