Problem Solving

Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
2/5
7/15
1/2
8/15
3/5

OA [spoiler]3/5[/spoiler]

The answer is 3/5.
You mark the pieces at 1/5ths and 1/3rds.

You get portions of 20%
40%
60%
80%
100%, by 1/5th Markings.

and 33.33%
66.66 %
and 100%, by 1/3rd markings.(Both on the same branch of course)

now you cut it at these portions:
You get 20% piece(at 1st 15th marking)
then 13.33 % piece(at first 1/3rd marking)
and 6.77% piece.(at second 1/5th marking)
All the remaining portions repeat the trend.
You can better explain the problem to yourself by drawing it on your note!

The remaining is from 40% to 100%= 60% of the original branch.
Hence, 3/5.

Another great explanation, Winnie! Just one more way to look at this - since they give it to you in fractions and the answers are in fractions, I'd look at this as a common denominator problem. You have markings each 1/5 and 1/3, or every 3/15 and 5/15. So you have markings at:

0, 5/15, 10/15, 1
0, 3/15, 6/15, 9/15, 12/15, 1

And since it's all common denominators you're at:

0, 3, 5, 6, 9, 10, 12, 1

So you have unique distances of 3, 2, and 1, so you'd remove 6 out of 15, having 9/15 or 3/5 left.

Just since you see that they're already using fractions to start it's not a bad idea to try finding common denominators...then you're only dealing with the integer numerators making the math pretty quick.

chaitanya.mehrotra wrote:Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
2/5
7/15
1/2
8/15
3/5

OA [spoiler]3/5[/spoiler]

Ignore the given length of 1-meter. The problem can be solved using any length.
Let length = 15 meters.
Dividing 15 into 3rds will yield markings at 5 and 10.
Dividing 15 into 5ths will yield markings at 3,6,9, and 12.

Listing the markings in order:
0......3....5..6......9..10....12......15

There are only 3 distinct lengths: 1 meter, 2 meters, and 3 meters.
Subtracting these 3 distinct lengths from 15, we get:
Length remaining = 15-1-2-3 = 9.
Remaining length/Total length = 9/15 = 3/5.

In my opinion, numbers are easier to deal with as compared to fractions.
Looking at the branch as a numberline and taking the length at 100cm
the thirds markings will be at
33.33 and 66.66
The fifths markings will be at
20, 40, 60, 80

Arranging them on the number line gives us
20, 33.33, 40, 60, 66.66, 80, 100
So the lengths of the pieces would be
20, 13.33, 6.66, 20, 6.66, 13.33, 20

Picking out each distinct length takes out 6.66+13.33+20 40. What remains is 100-40 = 60. Hence 3/5.