Addition and Subtraction problem

[Jasonator]

Just wondering if there's anyone here who can help me with this elementary school math problem. I know the answer, but I don't know the formula for solving such problems.

Problem: If you start reading a book from page 120 and stop at page 300, how many pages have you read?

The answer should be 181, but if you subtract 120 from 300, you get 180. So, obviously, that's not the right formula. Does anyone know the proper formula for solving this problem?

 

[AvgStudent]

Just wondering if there's anyone here who can help me with this elementary school math problem. I know the answer, but I don't know the formula for solving such problems.

Problem: If you start reading a book from page 120 and stop at page 300, how many pages have you read?

The answer should be 181, but if you subtract 120 from 300, you get 180. So, obviously, that's not the right formula. Does anyone know the proper formula for solving this problem?

Hi Jasonator,
You can try with smaller examples to figure out the equation.
If you read pages 2 to 3. How many pages did you read?
If you read pages 2 to 5. How many pages did you read?
If you read pages x to y. How many pages did you read?
Hope this helps

 

[Dr.Peterson]

Just wondering if there's anyone here who can help me with this elementary school math problem. I know the answer, but I don't know the formula for solving such problems.

Problem: If you start reading a book from page 120 and stop at page 300, how many pages have you read?

The answer should be 181, but if you subtract 120 from 300, you get 180. So, obviously, that's not the right formula. Does anyone know the proper formula for solving this problem?

If I want to find the number of pages in a chapter, say, I subtract the first page of the chapter from the first page of the next chapter.

In terms of the first and last pages read, this is (L+1)-F, or L-F+1.

Your error is so common that it has a name: off-by-one error. Specifically, look in the link for "fencepost error".

 

[Steven G]

From page 1 to page 10 is 10 pages.
From page 1 to page 123 is 123 pages.
From page 1 to page 17 is 17 pages.
We are experts in answering these type problems if we start with page 1. So let's also start with page 1!

Suppose you want to know how pages there are from page 7 to page 12. Like I said, start at page 1.
1 2 3 4 5 6 7 8 9 10 11 12.
Now from page 1 to 12 is 12 pages and it does include the pages you are concerned about ( 7 8 9 10 11 12) and some more pages.
You do not want pages from page 1 to page 6 which is 6 pages. So the answer is 12-6 or 6 pages.

If you want to know how pages there are from page 205 to page 220.
1 2 3 ... 204 205 206 ... 220.
From page 1 to page 220 is 220 pages and we want to remove pages 1 through 204 which is 204 pages. The final result is 220-204 = 16 pages.

In math, it is always best to use what you know well (like how many pages from 1 to 100 is 100 pages) and modify that to answer your question. Note that in my two examples above I never counted pages where the 1st page was not 1.

 

[Steven G]

Hi Jasonator,
You can try with smaller examples to figure out the equation.
If you read pages 2 to 3. How many pages did you read?
If you read pages 2 to 5. How many pages did you read?
If you read pages x to y. How many pages did you read?
Hope this helps

But this method that you are suggesting doesn't show why it works.
Why things work is what makes math fun.
Somethings in math are so 'obvious', but still wrong!

 

[AvgStudent]

But this method that you are suggesting doesn't show why it works.
Why things work is what makes math fun.
Somethings in math are so 'obvious', but still wrong!

Yes, you are right, but my intention was to help the OP arrive at "the proper formula for solving this problem". I couldn't explain to Jasonator why the equation works if the s/he doesn't know the equation to start with.

 

[Jasonator]

Thank you for your help, everyone!

 

[The Highlander]

Just wondering if there's anyone here who can help me with this elementary school math problem. I know the answer, but I don't know the formula for solving such problems.

Problem: If you start reading a book from page 120 and stop at page 300, how many pages have you read?

The answer should be 181, but if you subtract 120 from 300, you get 180. So, obviously, that's not the right formula. Does anyone know the proper formula for solving this problem?

The best way to 'explain' this to "elementary school" pupils is to slightly "re-word" the problem (rather than any complicated "Maths" at their stage).
Instead of thinking about how many pages they have read (as the question asks) suggest that they think about how many pages they haven't read!
They haven't read the first 119 pages out of the 300 (available) pages in the book, so subtracting 119 from the 300 gives the correct answer of 181 pages that have been read. ?
It's not so much that a "formula" is required, just some logical/lateral thinking. ?

 

[Steven G]

The best way to 'explain' this to "elementary school" pupils is to slightly "re-word" the problem (rather than any complicated "Maths" at their stage).
Instead of thinking about how many pages they have read (as the question asks) suggest that they think about how many pages they haven't read!
They haven't read the first 119 pages out of the 300 (available) pages in the book, so subtracting 119 from the 300 gives the correct answer of 181 pages that have been read. ?
It's not so much that a "formula" is required, just some logical/lateral thinking. ?

Please read post #4.

 

[The Highlander]

Please read post #4.

I did, Steven, and it's all perfectly correct (and sound mathematical thinking) but if you try presenting that to an elementary school class (just read your post out loud), half (if not most) of the pupils' attention will be well outside the window and down the street.
Whereas, having presented the problem, if you then just say to the class: "Think about how many pages you haven't read.", you immediately focus their attention on a new aspect of the problem that provides a simple "technique" they can acquire that will benefit them for the rest of their lives.
I did not intend to contradict anything you (or any other thread contributors) said and I trust no offence has been taken.