Tuesday, July 4, 2017

Precise Means of Online Equations - Explained

Several times we may have come across an online post or a fragment of a social media feed stating something such as `This math Problem is Stumping the whole Internet & Can You Solve It? Or Apparently 9 out of 10 people get this wrong. Do you know the answer?

‘At the core of the post there tends to lie numbers and symbols. Irrespective of how hard you may tend to try, it may seem impossible to accept the challenges. One may attempt to do so and on checking on the comment sector you are likely to get to know that some have agreed with your answers while the others tend to have a different point of view. The precise means of approaching these online equations with the least of hassle is explained below:

Language of Mathematics

We tend to read from left to right in the English language and hence it seems natural to view mathematical equations in the same manner. However one would not try to read Arabic or Mandarin in the same way nor would they try to do so with the discrete language of mathematics. In order to be maths-literate, it is essential to comprehend some of the applicable rules regarding spelling and grammar in mathematics.

A set of firm rules called the order of operations tends to express the precise arithmetical grammar wherein it conveys to us the system in which the mathematical operations need to be performed such as addition and multiplication when they both appear in an equation. The mnemonic BODMAS – Brackets, Order, Division, Multiplication, Addition, and Subtraction, in Australia tends to teach students in assisting them to recall the correct order.

In BODMAS, the order tends to refer to mathematical powers like squared, cube or square root. This could be taught in other countries as PEMDAS, BEDMAS or BIDMAS though all these may come down to precisely the same thing. For instance, it would mean that if we have an equation containing addition as well as multiplication we tend to carry out multiplication first irrespective of the order where they are written.
While considering the equations:
• (a) 3 x 4 + 2
• (b) 2 + 3 x 4
When BODMAS is applied we see that these equations are precisely the same or equivalent and in both the cases we tend to calculate 3x4=12 and then calculate 12+2=14. However some may tend to get an incorrect answer for the second equation since they would have tried solving it from left to right. They may do the addition first (2+3=5) and thereafter multiplication of (5x4) in order to get a wrong answer of 20.

Brackets tend to make a difference

It is here where the brackets tend to be beneficial segment of arithmetical punctuation. A well placed bracket in maths could change the calculation completely. They are utilised in providing a specific part of an equation and we always carry out the calculation within the bracket before dealing with what is outside the bracket. If brackets are introduced around the addition in equation in the above equations we then tend to have two new equations namely
• (c) 3x(4+2)
• (d) (2+3)x4

Correct Understanding of Operation

These equations are not equivalent to each other and in both the cases, the bracket conveys to us to carry out the addition before doing the multiplication. This would mean that we have to compute 3x6 for (c) and for (d) 5x4. We now arrive at different answers wherein the answer for (c) is 18 and (d) is 20. In the case of (a) and (b) equations brackets were not essential since BODMAS conveys to us to do the multiplication before addition.

But with the addition of brackets which reinforces the BODMAS rules could be helpful in evading confusion. Comprehending BODMAS is likely to get us most of the way with regards in resolving the problem though it also assists in being aware of the commutative as well as the associative properties of mathematics. Calculated process is said to be commutative if it is not considered in which order the numbers are said to be written in and addition is commutative since a+b=b+a. However subtraction is not a commutative since a-b is not the same as b-a.

Moreover it is also direct to display that multiplication is commutative while division is not. An operation is said to be associative when we have numerous successive incidences of this type of operation and it does not matter to which order we carry them out.

Moreover addition as well as multiplication seems to have this property and though subtraction together with division does not have the same. Once the understanding of the correct order of operation together with the associative as well as commutative properties has been arrived we tend to have the tool-box in solving any well-defined arithmetical equation.