How can we visualise fractions within fractions, what is the correct wording. (Banned member)

[Cambridge101]

We learn that if I have 2/3, this in words is I have a whole split into 3 bits and I have 2 of these bits. Thus, I have 2 of the total 3 thirds. Thus two thirds = 2/3.

So in words, the definition of a fraction is, when a whole has been split into equal parts, and we have some x amount of them. This definition is great when the numerator and denominate are whole numbers.

But then if I have say 2/11 / 5/7. We say we can generate and equivalent fraction by manipulating the numerator and denominator by the same amount. We say this because 2/11 / 5/7 is identical to some other fraction. In this case, 14/55. But my question is, how can we see this. How would you explain in plain english what 2/11 / 5/7 is.

It makes no sense to word it like a whole split into 5/7 (correct me if I am wrong), because this would no longer be a whole. So when I say 2/11 / 5/7 , in plain english the previous definition of a fraction does not fit. How can we say 2/11 / 5/7 is identical to 14/55 if we cant see in the physical world what 2/11 / 5/7 is..... to me, it is just very unsatisfactory to say we can do it because equivalent fractions work for whole numbers, thus it must work for decimals, because i cant visualise it literally.

Any thoughts,

Cheers

 

[lookagain]

We say this because 2/11 / 5/7 is identical to some other fraction. In this case, 14/55.

No, (2/11)/(5/7) = (2/11)*(7/5) = (2*7)/(11*5) = 14/55.

What you wrote is not equal to 14/55 due to the Order of Operations.

How would you explain in plain english what 2/11 / 5/7 is.

Any thoughts,

"English" is capitalized. For an explanation of what you intended for your expression, please see the above comment.

 

[Cambridge101]

No, (2/11)/(5/7) = (2/11)*(7/5) = (2*7)/(11*5) = 14/55.

What you wrote is not equal to 14/55 due to the Order of Operations.




"English" is capitalized. For an explanation of what you intended for your expression, please see the above comment.

Um.... type 2/11 over 5/7 in a calc and you get 14/55
2/11 / 5/7 = 2/11*7/5 = 14/55?

There is no need for brackets mate, you know what I am talking about. I know BIDMAS, so does my fish!

And why are you commenting on the capitalisation of English pahahaha

I will wait for a helpful response i guess or I will just repost this.

 

[lookagain]

Um.... type 2/11 over 5/7 in a calc and you get 14/55
2/11 / 5/7 = 2/11*7/5 = 14/55?

There is no need for brackets mate, you know what I am talking about. I know BIDMAS, so does my fish!

And why are you commenting on the capitalisation of English pahahaha

I will wait for a helpful response i guess or I will just repost this.

Cambridge101, no, type in 2/11/5/7, and it would give .00519..., because it
evaluates division from left to right.

2/11/5/7 = (2/11)/5/7 = (2/(11*5))/7 = (2/55)/7 = 2/(55*7) = 2/385

When you write the problem out in horizontal style, you must have grouping
symbols around 5/7. For more readability and consistency, the grouping
symbols may be placed around 2/11.

You do not know BIDMAS well enough, because the divisions are done from
left to right.

I corrected your spelling of "English," because you made it a point to state
"plain english," which is ironic.

I am not your "mate." You can address me by my username "lookagain" or
not address me. In writing away from this forum, if you decide to address
someone by "mate," you place a comma immediately in front of it.

Example: "I understand what you said, mate."

 

[Cambridge101]

I will repost the question for someone who can provide helpful explanations.

 

[AvgStudent]

One way you can think of it is you start with 2/11 of a pizza, then you wish to divide 2/11 by 5/7 people. Which is synonymous with (2/11)*(5/7).
In order words, you're taking 2/11 of the pizza you start with, times 5. Now, you have 10/11 of the pizza and divide it equally among 7 people. Not sure if this helps.

 

[Steven G]

pka is 100% correct. You wrote 2/11 / 5/7 as you did (with the spacing of that middle division line) since you know that 2/11/5/7 is not the same as (2/11)/(5/7).
I had a nice video to recommend to you but since you are were so condescending in your reply to pka I choose not to give you the link to the video