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Nairaland Forum / Nairaland / General / Education / Basic Arithmetic; A Response To Bluntnigerian's Thread. (1117 Views)
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Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 10:02pm On Sep 08, 2020 |
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... 1 Like |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Emmyth(m): 10:06pm On Sep 08, 2020 |
Waiting. . |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 10:31pm On Sep 08, 2020 |
No matter what your teachers thought you in primary or secondary school, if your workings defy this set of rules and you don't get the answer determined by them, you have failed by the standard of Mathematics. GROUPING SYMBOLS. Grouping symbols determine the order in which an arithmetic expression is to be evaluated. Group symbols are: (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. If a fraction bar occurs in an arithmetic expression, you "clear it" as the grouping symbol that it is by evaluating its numerator and denominator following STEP 2 - 4 in order, and then you divide. Remember you must first evaluate all expressions in grouping symbols working from inside to outside. If you don't understand, tell me and I will explain in detail. 1 Like |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 10:48pm On Sep 08, 2020 |
▪︎If a grouping symbol is "attached" to a number or another grouping symbol, multiplication is implied. For example 2(3 + 4) means 2 × (3 + 4) (3 ÷ 5)(5 – 1) means (3 ÷ 5) × (5 – 1) [4² + 3](4 × 7) means [4² + 3] × (4 × 7) {3 + 3 ÷ 3}[2 ÷ 4][4 × 7] means {3 + 3 ÷ 3} × [2 ÷ 4] × [4 × 7] This applies to all grouping symbols and any possible combination of them. |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by ymstar(m): 12:21am On Sep 09, 2020 |
This is the kind of thread we want abeg 1 Like |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by RubiesBanking: 1:09am On Sep 09, 2020 |
Honestly that thread really surprised me, simple math calculation for that matter. |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by BluntNigerian: 9:43am On Sep 09, 2020 |
Martinez39s:Now, you took up the matter fully?? That's Wonderful.. Remember to add the photo of the two calculating devices, so as to make the thread interesting. .. Now, we move on. Isn't it?? |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by BluntNigerian: 9:43am On Sep 09, 2020 |
Lalasticlala |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by BluntNigerian: 10:09am On Sep 09, 2020 |
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. |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 11:17am On Sep 09, 2020 |
BluntNigerian: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. 1 Like |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Newman20(m): 9:18pm On Feb 21, 2021 |
Hey, Martinez39s I wanted to ask if you could make more arithmetic threads. |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 12:16pm On Jun 12, 2022 |
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. hazard7: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. hazard7: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. 1 Like 1 Share |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by hazard7(m): 1:02pm On Jun 12, 2022 |
Martinez39s: Ok thanks man |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Femzaremz(m): 7:24pm On Jun 13, 2022 |
Martinez39s:this is a universal experience for everyone who has ever trained before! |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 4:15am On Jun 28, 2022 |
.... |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by MrHighSea: 10:44am On Jun 28, 2022 |
All I see is BODMAS |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Adasun(m): 10:55am On Jun 28, 2022 |
MrHighSea:I think using bodmas would give u one |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Adasun(m): 11:07am On Jun 28, 2022 |
on step one,they are two grouping symbols- the bracket and the division. how do u know Which to start with? |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Adasun(m): 11:20am On Jun 28, 2022 |
when u said"working from the inside out" do u mean from right to left? martinez39s |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 4:37pm On Jun 28, 2022 |
Adasun:Quote the post you are referring to. |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 4:42pm On Jun 28, 2022 |
Adasun:Nope. It means evaluating the expressions confined by the innermost grouping symbols first. After that is done, keep repeating until you clear all the grouping symbols. Do you understand or should I exemplify my point with examples? |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Adasun(m): 1:36pm On Jun 29, 2022 |
Martinez39s: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? |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Adasun(m): 1:37pm On Jun 29, 2022 |
Martinez39s: |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 8:12pm On Jun 29, 2022 |
Adasun: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. |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Adasun(m): 6:48pm On Jun 30, 2022 |
Martinez39s:but they both perform the same function right? |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Martinez39s(m): 7:48pm On Jun 30, 2022 |
Adasun:They perform the same function, but the division sign is not a grouping symbol. |
Re: Basic Arithmetic; A Response To Bluntnigerian's Thread. by Adasun(m): 4:07pm On Jul 01, 2022 |
Martinez39s:OK. thanks alot 1 Like 1 Share |
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