(1) Parentheses ( ). "Parentheses" is North American English. In British English, and consequently in this country, parentheses are simply called brackets or round brackets.

(2) Brackets [ ]. In British English, this is referred to as square bracket.

(3) Braces { }. Most of us who studied Set should be familiar with braces. Braces are also grouping symbols in arithmetic.

(4) Fraction bar – . The fraction bar is used when we write fractions. The numerator stays on top of the bar while the denominator stays below.

Martinez39s:
Recently, a nairalander BluntNigerian tabled a problem involving basic arithmetic which confounded him in this thread of his. His problem was that he obtained 9 and 1 as answers to 6 ÷ 2(2 + 1) from his android calculator and calcio calculator respectively. In his opinion, the makers of android ought to be sued.

One would have thought the many maths literate in this section would have educated him on this issue and pointed out the correct answer to him but things took a shocking turn. Some people said 9 and 1 are both correct, and some people agreed with them. More shocking was a supposed Engineer and Physics teacher agreeing with this. Some even said 1 is the correct answer. In this thread of mine, I will like to educate the readers on the order of arithmetic operations.

When solving an arithmetic problem, there is a conventional set of rules one must adhere to in obtaining an answer. This conventional set of rules eliminates any ambiguity an arithmetic expression could possibly present. For example, how do you solve 6 + 2 × 3? Do you add first or multiply first? What is the difference between 6 ÷ (2(2 + 1)) and 6 ÷ 2(2 + 1)? As you would see, the conventional set of rules which is called ORDER OF ARITHMETIC OPERATIONS will help us answer these questions. This set of rules is the standard; this means there can't be two answers to an arithmetic expression. There can be one and only one answer.

ORDER OF ARITHMETIC OPERATIONS
This lists out the order you must take in solving an arithmetic expression. The order is as follows:
STEP 1: perform all calculations within grouping symbols following the order listed from STEP 2 - 4, working from the innermost pair of grouping symbols to the outermost pair. Group symbols are parentheses, square brackets, braces, and fraction bars. I will later explain grouping symbols in details.
STEP 2: evaluate all exponential expressions and roots.
STEP 3: perform all operations of multiplication and division as they occur from left to right.
STEP 4: perform all operations of addition and subtraction as they occur from left to right.


Typing...

BluntNigerian:
You know,, the whole of 2(2+1) is the denominator..
Or, can you explain that further too??
Thanks
...
Let's see this...
20 ÷ 5(2x + 3)=5...
Find x.
Show your workings.

hazard7:
Hi guys, its been a while. Big thumps to the guys still keeping this space alive.
To the workout enthusiast in the house. It's been long since I workout so I decided to yesterday and my calf workout literally gave me a huge ache in my leg now I can't work and I think I have muscle sprain so who has experience this before and how did you solve it?.

hazard7:
Thanks man, truth is I can't even walk properly without limping

Martinez39s:
NB: I had to bring our discussion here and remove my post in the red pill thread. I HAVE COMMENTED ON YOU SECOND POST HERE.

if you haven't worked out in a long while, the level of soreness you will experience when you resume is similar to that of when you first started gyming. On the other hand, the soreness you feel when you have been working out regularly isn't that much; it's as if your body has gotten used to the training.

Try to rest. Muscles must be given time to heal. You will be alright. Don't rush things; rest and recovery are very important in achieving your goals.

It happens. The first time I gymed (upper body workout), my muscles were so sore that I almost couldn't wear my shirts or take off my T-shirts.

When I first did thorough leg workouts, I felt pains in my leg, especially the calfs and thighs. I couldn't walk properly and it was as if my inner thighs were on fire; I was restless and could hardly sleep. My knees felt sharp pain when bent down to squat.

Martinez39s:
NB: I had to bring our discussion here and remove my post in the red pill thread. I HAVE COMMENTED ON YOU SECOND POST HERE.

if you haven't worked out in a long while, the level of soreness you will experience when you resume is similar to that of when you first started gyming. On the other hand, the soreness you feel when you have been working out regularly isn't that much; it's as if your body has gotten used to the training.

Try to rest. Muscles must be given time to heal. You will be alright. Don't rush things; rest and recovery are very important in achieving your goals.

It happens. The first time I gymed (upper body workout), my muscles were so sore that I almost couldn't wear my shirts or take off my T-shirts.

When I first did thorough leg workouts, I felt pains in my leg, especially the calfs and thighs. I couldn't walk properly and it was as if my inner thighs were on fire; I was restless and could hardly sleep. My knees felt sharp pain when bent down to squat.

MrHighSea:
All I see is BODMAS

Adasun:
on step one,they are two grouping symbols- the bracket and the division.

how do u know Which to start with?

Adasun:
when u said"working from the inside out" do u mean from right to left?


Martiñez39s

Martinez39s:
For your question 6 ÷ 2(2 +1), you need to have it in mind that grouping symbols imply multiplication as I pointed out.

6 ÷ 2(2 + 1) = 6 ÷ 2 × (2 + 1)
= 6 ÷ 2 × 3 STEP 1
= 3 × 3 = 9 STEP 3 (there are no roots and exponents so we moved on to step 3).

If 2(2 + 1) was the denominator of your question, the right expression would have been 6 ÷ (2(2 + 1)). You answer here would have been 1.

As to your question, 20 ÷ 5(2x + 3) = 5. You treat the expression in the brackets as a single number, say y. So let's say 2x + 3 = y.
20 ÷ 5(2x + 3) = 20 ÷ 5(y) = 20 ÷ 5 × y
20 ÷ 5 × y = 4 × y STEP 3

4 × y = 4y = 4(2x + 3)
4(2x + 3) = 8x + 12 (distributive property.)
8x + 12 = 5
8x = 5 - 12 = –7
x = –7 ÷ 8 = –(7/8 )

I actually don't know what you are driving at with the solution to an algebraic equation in one variable.

Martinez39s:
Quote the post you are referring to.

Adasun:
in your calculation, u started with 2 +1 inside the brackets, but they is also division which fall under grouping symbols as u said.


my question is, if they are more than one grouping symbol,how do you know which to begin with.


in the first example,if I start by dividing 6 by 2 before attacking the brackets, is it a wrong move?

Martinez39s:
The division sign ÷ is not a grouping symbol. The fraction bar which separates the numerator and the denominator in a fraction is a grouping symbol.

Adasun:
but they both perform the same function right?

Martinez39s:
They perform the same function, but the division sign is not a grouping symbol.