Square root of 64 divided by 1/2 times 2 = ? Many don’t get this BASIC Math!

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[ronrice]

I think we all agree that this is a poorly written expression that could be interpreted more than one way:
8 ÷ 1 / 2 x 2 = 8 / 2 x 2 = 4 x 2 = 8
8 ÷ (1/2) x 2 = 16 x 2 = 32

[alex-qeqn]

The method taught to me in Scotland over 65 years ago gives the answer 32; but I think that different countries etc. may have different methods of applying operators - clearly, we need to have universal agreement on operators — and a more liberal use of brackets/parentheses would be sensible.

[kjellg]

Forget about PEMDAS, it is not always crystal clear. Use parentesis so expressions are not ambiguous. The purpose is not to make traps, but to wright your expression in such a way that they are not misinterpreted by the reader.

[MusicNewb]

Communication is important in math. Any expression should be conveyed without ambiguity.

[whoff]

Tricky question.

It is explained only in the text form of the question "divided by 1/2" which is clearly equivalent to "*2".

But in the formular you find "÷1/2"
where "/" is just a sign for division
(without brackets). So according to PEMDAS it is first "divide by 1" then "divide by 2".
And this is sth. totally different from the first case.

[SodalisUK]

As written the formula is confusing as to whether 1/2 represents the number 0.5 or the partial formula 1 divided by 2. If you assume that / is the same as ÷ then the answer is 8 - if you assume that the 1/2 represents a number then the answer is 32.

[dave-in-nj]

to rewrite the problem :
8 / 1/ 2 * 2
now, do the math again.
just because you use two different division symbols does not alter the sequence.

[notme]

The '/' character is not included anywhere in PEMDAS. This explanation only works if some additional rule makes a fraction written like '1/2' a number which in this case is equal to one half. There seems to be an unwritten assumption that separating the fraction from the rest of the expression with spaces front and back means it should be read that way. Maybe such a conventions exist in the minds of some people, but I've never heard of it, and the result is very confusing. This should be taught as something to be aware of, but is actually a mistake.

If your aim is to explain to someone how to do this calculation using a typical calculator, don't tell them to divide by one half. Presumably, you know what the meaning of the expression is, so just tell them to multiply by 2. If it's some more fancy calculation, just tell them what keys they need to press.

When writing on paper, fractions can be more clearly written with a horizontal line drawn under all of the numerator and over all of the denominator. The universally recognized convention that this implies parenthesis around the fraction allows PEMDAS to be applied, eliminating any ambiguity.

When entering an expression into some document, explicitly use parenthesis - in this case '(1/2)' - if no other method is available. Teachers of written style, always prefer clarity, and not making the reader strain to understand the meaning of a sentence. Clarity is all the more important when writing on a mathematical subject.

Another comment here notes that that the unicode ½ could be used in text. The writer would have to get the ½ from the list of symbols in whatever document editor they are using, but the result would be compact, and could be visually more appealing. Like the '/' character, these special characters are also not included in the PEDMAS rule, but the meaning would be perfectly clear in my opinion. When writing on paper, the fraction could be written in a similar way, and that would be just fine too.

When writing an arithmetic expression in a computer program, usually the PEMDAS rule applies. Generally however, '÷' cannot be used, and instead, '/' is used to indicate division. This means that the '/' in the fraction will be handled left to right, the same as the other divisions and multiplications in the expression. To stop this happening, the fraction must be in parenthesis. If you let your students think it is ok to write expressions like the example in the video, they could be mightily confused when they later have a go at programming.

[jeremyhorne]

Okay… first, the obelus used after the sqrt64 doesn’t mean “divided by” but means “grand divided by”
So, we rewrite the problem with parentheses as
(Sqrt64) / (1/2x2)
Next, the slash between the 1 and 2 means “divided by” and does NOT denote a fraction. So, we simplify on both sides of the obelus.
Sqrt64 = 8
1/2x2 = 0.5•2 = 1
Finally, we perform grand division last by rule.
8 / 1 = 8
Of you had used the simple slash for division (the original symbol, btw) you would have
Sqrt64 / 1 / 2 x 2
That would be 8/1/2x2
Left to right that’s
8/1/2•2
8/2•2
4•2
8
To get the steps and result you showed, you would need to not only use simple division (slash) after sqrt64 but you would also need to write one half as a fraction instead of using simple division (slash) or put it in parentheses to begin with of that’s what you meant and you don’t have the ability to write it as a fraction.

[petersearls]

In your other examples when specifying fractions you don’t use “/“ you use “-“ as in 1 over 2. Here you are using the commonly accepted division symbol so by your own standards the answer would be 8 not 32.

[robertdeland]

You said that 1/2 should be treated as if it is parenthesized. Why? How would I know that? Pemdos doesn't say that.

[nathanw]

Only a teacher or exam writer would structure a fraction and ÷ symbol in an equation. First you run the risk that you have written it wrong and two you risk the reader interprets your intention incorrectly. Order of operations should be kept simple. People should not be guessing what is in the denominator and what is in the numerator. In my line of work, I would fire someone if I saw a calculation setup like this one. It could be so much clearer when written algebraically - no need for order of operations except for the square root.

[stevenjohnson]

Simple c 32 getting there is easy ✓64 primary root 8 dividing and fraction invert and multiply creating 16*2=32

[allanpatterson]

Order of operations with no brackets. Good review. I remember the FOIL rule with y=mx + b.

[perssoh]

NEVER ever use different symbols for division. If you used / only the anwer is 8.

[heatherbartusch]

Yes. PEDMS. In my head and by calculator. Thank you for all your videos. They are indeed helpful.
Bless you.

[kitcarsoncarson]

I think the way you pose the question matters. Just throwing numbers up there without grouping symbols and then change it when you begin to solve is the definition of trickery. There's always going to be someone who sees it the way you do without grouping symbols. But the whole point in using grouping symbols is to have everyone on the same page. I too would have said 8 but with grouping symbols I would have said 32 if the grouping symbols said that. All of math is important not just numbers that's why we have rules such as unless there's a (-) sign, it's (+).

[HugoRH]

Very easy. I don't understand people's confusion.
Square root of 64 is 8
8 divided by 1/2 is like multiply it by 2, so 8x2 is 16
Then 16 times 2 equals 32.

[maxhenderson]

I'd argue that there are six possible solutions: ±2, ±8, ±32 (depending on how the ambiguously written problem is interpreted).
This problem is written extremely ambiguously. Let me walk you through my logic and reasoning:
1. We all agree that √64 is 8
2. The √64 is also -8, so another solution for each interpretation is possible.
3. The use of both ÷ and / symbols is simply careless. These symbols mean the same thing, so you should stick to one division symbol.
4. Lack of parentheses/brackets surrounding 1/2 causes issues because you dont know whether its supoosed to be ((8÷1)/2)*2 or 8÷(1/2)*2
5. More issues arise since you dont know whether the problem is (8÷1)/(2*2), same with 8÷((1/2)*2) and 8÷(1÷(2*2)).

[Kualinar]

It's C, 32
Square root of 64 is 8. Dividing by one half is the same as multiplying by 2, so, 16. Then, multiply be 2 = 32. A few second in my head.

I sometimes use PERDMAS instead of PEMDAS. Parentheses, (exponent and radical), (division and multiplication), (addition and subtraction)