Question

\[\frac{3}{14}+\frac{10}{21}\div \left(\frac{3}{7}\right)\left(\frac{9}{4}\right)=\]

Answer 1

What is the answer?
Symbolab gives two: 58/81 and 9/17

The second one isn't in the original format though. ❓❓

Answer 2

This one looks real fun, sec

Answer 3

Er I meant 19/7 for the second one. Typo.

Answer 4

So they are as follows:

Answer 5

Wolfram gave 19/7

Answer 6

Same but it has the incorrect format (compared to OG question)

Answer 7

What do you mean by original format?

Answer 8

It's not written in the same format as the original given question.

Answer 9

I did get the same answer while solving on my own but if the format doesn't match it's not the same problem/exercise is it?

Answer 10

I'm honestly confused, 19/7 is a fraction and this problem is about fractions.

Answer 11

Honestly what did you do at 3/14 + 40/81

Answer 12

ho

Answer 13

ig I have to do the big #s

Answer 14

Okay I just solved it by hand and added parentheses around 3/7 and 9/4 in wolfram, for both I got 803/1134.

Answer 15

\[\frac{ 3 }{ 14 } + \frac{ 10 }{ 21 } \div ((\frac{ 3 }{7})( \frac{ 9 }{4 }))\]

Answer 16

\[\frac{ 3 }{ 7 } \times \frac{ 9 }{ 4 } = \frac{ 27 }{ 28 }\]
\[\frac{ 10 }{ 21} \div \frac{ 27 }{ 28 } = \frac{ 10 }{ 21} \times \frac{ 28 }{ 27 } = \frac{ 10 }{ 3 } \times \frac{ 4 }{ 27 } = \frac{ 40 }{ 81 }\]
\[\frac{ 3 }{14 } + \frac{ 40 }{ 81} = \frac{ 243 }{ 1134 } + \frac{ 560 }{ 1134 } = \frac{ 803 }{ 1134 }\]

Answer 17

... wait what?
Sorry I was multitasking @Shadow

Answer 18

There's no parentheses around those two fractions, lol

Answer 19

Yeah I did that to show how I approached PEMDAS

Answer 20

I did the multiplication first, then division, then addition

Answer 21

Unless in your hw it has that fraction over the other fraction

Answer 22

The answer in the book is \[\frac{19}{7}\]

Answer 23

Which is what I got but when I put it into Symbolab it comes up as \[\frac{58}{81}\]

Answer 24

K then I guess it has to be done division first.

Answer 25

I legit have no idea where you got that from tho lol

Answer 26

Here's the one that has the "proper format" --

Answer 27

Yeah did the division first and got 19/7

Answer 28

I guess the division puts emphasis since that fraction is under the second one, then you multiply it with the 4th, then add the product with the first fraction.

Answer 29

Under? 🤔

Answer 30

\[\frac{ \frac{ 10 }{ 21} }{ \frac{ 3 }{ 7 } }\]

Answer 31

Oh so you mean it ends up looking like this?\[\frac{3}{14}+\frac{\frac{10}{21}}{(\frac{3}{7})(\frac{9}{4})}\]

Answer 32

--
confusion

Answer 33

I'll just show my steps

Answer 34

Is what I put wrong?

Answer 35

The last equation thing I eman

Answer 36

mean*
Argh typos

Answer 37

\[\frac{ \frac{ 10 }{ 21} }{ \frac{ 3 }{ 7 } }\ = \frac{ 10 }{ 21} \times \frac{ 7 }{ 3 } = \frac{ 10 }{ 3 } \times \frac{ 1 }{ 3 } = \frac{ 10 }{ 9 }\]
\[\frac{ 10 }{ 9 } \times \frac{ 9 }{ 4 } = \frac{ 10 }{ 1 } \times \frac{ 1 }{ 4 }= \frac{ 10 }{4 }\]
\[\frac{ 3 }{ 14 } + \frac{ 10 }{ 4 }= \frac{ 6 }{ 28 }+ \frac{ 70 }{ 28 } = \frac{ 76 }{ 28 } = \frac{ 19 }{ 7 }\]

Answer 38

This way gives the correct answer.

Answer 39

So you'd put parentheses around the middle fractions. Apparently if you do the last two fractions first then divide, it gives the incorrect answer???

Answer 40

Apparently it has to do with PEMDAS being left-right if the P and E are nonexistent.

Not sure -- does the parenthetical part at the end not count as P?

Answer 41

I think I see the problem with Symbo, it's putting 3/14 on the top when it should be to the side

Answer 42

\[\frac{3}{14}+\frac{10}{21}\div \left(\frac{3}{7}\right)\left(\frac{9}{4}\right)=\]\[\frac{3}{14}+\frac{10}{21}\times(\frac{7}{3})(\frac{4}{9})\]This would work too, right?

Answer 43

Yes, that's what I did but in that instance you'd have to do the middle fractions after flipping the reciprocal, since you're doing the division, then you can go to the last fraction.. then add.

Answer 44

Testing.\[\frac{3}{14}+\frac{10\times7\times4}{21\times3\times9}\]\[\frac{3}{14}+\frac{10\times4}{3\times3\times9}\]

Answer 45

Sorry, too lazy to put equals signs because I'm afraid my train of thought will derail. 😂\[\frac{3}{14}+\frac{40}{9\times9}\]\[\frac{3}{14}+\frac{40}{81}\]...Okay maybe it wouldn't work.

Answer 46

Yeah then you're doing what I did earlier, with 1134 in the denominator.

Answer 47

\[\frac{3}{14}+\frac{10}{21}\div \left(\frac{3}{7}\right)\left(\frac{9}{4}\right)=\]\[\frac{3}{14}+\frac{10}{21}\times(\frac{7}{3})(\frac{9}{4})\]Then this?

Answer 48

Basically removing the \(\frac{9}{4}\) as it's not part of the current operation being used

Answer 49

And then integrating it back in later. I think the issue is that the method getting the giant fraction result is because the last 2 fractions are still essentially getting multiplied first

Welp

Answer 50

Yeah I think book is assuming parentheses around 10/21 div 3/7

Answer 51

Because you need to do that first to return 19/7

Answer 52

When we multiply across we get a nasty fraction.

Answer 53

There was actually a consecutive question that asked you to explain the order of operations you'd undertake.

It didn't say that, but it did say PEMDAS without P & E = left-to-right.

Answer 54

It didn't say "parentheses" in the answer key* oops

Answer 55

Honestly I thought it didn't make a difference when there's multiplication and division. Thought they had the same priority. I don't remember left to right lol.

Answer 56

But that would explain the priority.

Answer 57

I wonder why Symbolab put that answer for a question written in the original format, i.e. \[\frac{3}{14}+\frac{10}{21}\div \left(\frac{3}{7}\right)\left(\frac{9}{4}\right)=\]

Answer 58

But the correct answer had a different way of writing entirely

Answer 59

I mean:

Answer 60

Was it to emphasize the special rule of PEMDAS in this scenario...? Confusin

Answer 61

Yes it's taking it left to right.

Answer 62

So when they have the same priority like M/D or A/S, you go left to right

Answer 63

Yeah, but I don't see why they couldn't have made that format step 2. I legitimately thought that was something else entirely

Answer 64

Can't just do the multiplication first.

Answer 65

It's the parentheses. Trick shot. 🥴

Answer 66

I mean I probably did the thing with division-first but I had a full-on argument with someone over the fallibility of SL oops. 😂😂

Answer 67

Well technically there's no parentheses, it's just saying according to PEMDAS + left to right, need to do the division first, so it's pseudo parentheses if you mean as a term for priority.

Answer 68

Oh

Answer 69

Lmao

Answer 70

Yeah, pseudo.

Argh, this was so stupid xD

Answer 71

Yeah well honestly I learned something here so ig I'm grateful you asked.

Answer 72

I haven't done an actual math class in like 2yrs

Answer 73

Feels more like a hardcore review LOL

Answer 74

Because technically those parentheticals mean multiplication yet look like actual Ps from PEMDAS. 🤦🏻‍♀️

Answer 75

Guess Symbolab got confounded 🥴

Answer 76

I mean, I get it, the issue was just me thinking that Symbolab had to be right so I was trying to prove it

Whoops

Answer 77

I did some quick math to illustrate the rule:

\[\frac{ a }{ b } \div \frac{ c }{ d } \times \frac{ e }{ f } = \frac{ a }{ b } \times \frac{ d }{ c } \times \frac{ e }{ f } = \frac{ ade }{ bcf }\]

\[\frac{ a }{ b } \div \frac{ c }{ d } \times \frac{ e }{f } = \frac{ a }{ b } \times \frac{ df }{ ce } = \frac{ adf }{ bce }\]

First one I did division of the first two terms first. Second one I did multiplication of the last two terms first. They return different results.

Answer 78

And left to right aka div first in this case is the right way.

Answer 79

Maybe Symbolab isn't applying the left to right rule? idk

Answer 80

Honestly it's a literal WTH moment like.
If it had gotten the 1134-denominator fraction I would have accepted it as a glitch in the system, but not THIS.

Answer 81

I have no idea where this came from. It was so outrageous I started questioning if I had done something wrong lol

Answer 82

ig, but sometimes your teacher gives you problems with unpretty solutions. I don't know your prof so I just accepted the result, but I've learned now I gotta do left to right lul.

Answer 83

I think we got it though.

Answer 84

Oh it's not me, it was someone else

Answer 85

The math engines are just computing things with an odd priority

Answer 86

I'm way past this level but Symbolab threw me for a loop. I need to stop believing in the infallibility of technology lol.

Answer 87

I think the problem is the divisor, they assume 3/14 is on top with 10/21, and that 3/7 and 9/4 are on the bottom. Or some other other combination where 3/14 is outside.

Answer 88

See what I mean?

Answer 89

Rather weird bc there aren't ANY parenthetical indicators. Like... what even.

Answer 90

Yeah so by hand I would've had this, but I thought I got auto-corrected WHOOPS.

Answer 91

Yeah ig the engines are sometimes weird.

Answer 92

Entire point of this thread: don't trust the internet LOL
Alright thanks for putting up with that xD

Answer 93

This is why I usually put parentheses around my fractions, so they don't spill into each other.

Answer 94

Too much to ask for a medal? 🥴

Answer 95

🙏🏻

Answer 96

I feel like I ran into a similar issue of some other algebraic principle last week. I should go look for it and figure out why there was a disparity in that one...

Answer 97

Found it

Answer 98

Oh wait, that's a word problem. 🤪

Answer 99

Anyway thanks for helping me figure out how faulty modern internet can get. I'll stop pestering you with pings now

Answer 100

It was a pleasure.