Expert: Ahmed Salami - 12/8/2011

Question
QUESTION: Hello:

How should this calculation be solved?

(1/7)/ 15 X 21 = ?

If I have calculated properly, 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?

I thank you for your reply.

ANSWER: Hi Kenneth,
Well, you can always use the BODMAS order of operations which in full is;
B = Brackets
O = of
D = Division
M = Multiplication
A = Addition
S = Subtraction

And so the correct way to evaluate (1/7)/15 x 21 would be
(1/105) x 21 = 1/5

Regards

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply.

Consider this calculation. It is similar to my first one.
(7)/14 X 21 = ?

If 7 is divide by 14 and then the result multiplied by 21, the result is 10.5. I do not think that 10.5 is the correct answer. I think the correct answer is 1/42.

I used the same method to determine the answer as you used in the first calculation. Why did dividing 7 by 14 and then multiplying by 21 equal the incorrect answer?

I thank you for your follow-up reply.

Answer
Hi Kenneth,
Since you have two mathematical operators the first one to use would be the division D because it comes before multiplication M in the BODMAS order.
So,
7/14 x 21 = (1/2) x 21 = 10.5

It would be different if it was 7/(14 x 21) as that would be 7/294 = 1/42

The thing you should realise is that at times people might write expressions in ways that wouldnt represent the correct evaluation they intended. But it wouldnt be your mistake if you followed the standard way of simplification. What i'm saying is that if someone writes 7/14 x 21 then its mathematically 10.5 and the correct use and placement of the operators (especially the bracket sign) is the responsibility of whoever is writing the expression.

Regards