What patterns do you see in this string. Describe how you see in this string. Can you find 3 or more?
Todays test asked 1/2 +1/3 does not equal 2/5. What evidence did you use to convince me?
Leave a comment. Thanks (58 comments yesterday. Lets have more today.
17 comments:
Patterns I noticed are
1.the first three fractions go up by doubling the denominator and what it equals to goes down dy dividing the 12 by 2 then the 6 by 2.
2.1/4 of 12=3 and 1/2 of 6=3
1/2 then double teh denominator to 1/4 and 6 doubled to 12 but it equals the same number, 3.
3.the number is divided by the denominator
e.x 1/2 of 24=12 24 divided by 2= 12.
The Math Test:
My First Theory Waz That You Can Add The Numerator By The Numerator.
So the New Numerator would be 2.
Then Add The Denominator To The Denominator.
So The New Denominator Would Be 5.
So That It Would Equal=2/5
Then My Second Thoery I drew A Picture And It Didnt Really Work Out
the patterns that i saw are
1. 1/4 of 12= 3 1/2 of 6=3
1/2 is just dubbling. the answer the same.3 and 3
2. 1/2 of 24=12
1/4 of 24=6
1/8 of 24=3
the denominators are doubling each time. the answers are decreasing by half each time.
3. 1/4 of 24=6
1/8 of 24=3
the denominator os 1/4 is doubling and the answer is half of 6.
The Math Test:
1)first i added the numerator to the denominator. 1/0 + 0/3= 0/4
2)Then i added the denominator to the numerator. 0/2 + 1/0= 3/0
3)After that i added 3/0 to 0/4 so that it equaled 3/4.
And that was my awnser!
hello. again its jasmine . i accidently delted my own comment. ..
___________________________
1/2 + 1/3 = 3/5 because what you do to the bottom you got to do to the top
example::
1 ^ -> 1
- ^ -
2-> ^ 3
equals 3
___________________________
1-> v 1
- v -
2 v -> 3
equals 4
that makes 3/4
___________________
3/4 > 2/5 [[ > means greater than]]
3/4 is greater than 2/5 is because if you divide the numerator by denomanator 3/4 = 0.75 and 2/5 = 0.4
which makes 0.75 larger and it isnt equal!!!
-- jasminerose :) ☻☻♥♥☺☺♣♠♦◘○•!
edit. the picture i made didnt work!
this what i was trying to draw
http://i233.photobucket.com/albums/ee4/jasminerose_math/math.jpg
not hyperlinked so .. yeah
The Patterns That I Noticed Are:
1. The first three fractions in the string 1/2, 1/4, and 1/8 are going up by 2 as the denominator. What ever the answer is it goes down by dividing 12 by 2 then you do the 6 by 2.
2. 1/2 of 24 = 12
1/4 of 24 = 6
1/8 of 24 = 3
So if 1/2 of 24 is 12 you then half the answer of 12 and you get 1/4 of 24. Same with 1/8 of 24 it would equal 3.
3. 6 = 1/4 of 24
3 = 1/8 of 24
The number is divided by the denominator.
Math Test.
Well i said that it didn't equal 2/5 because you don't add the numerator and the denominator together. If the denominators were the same, you just add the numerators. If they are different you have to find a common denominator between the 2. Like 1/2 and 2/3 you need a common denominator for 3 and 2 (easiest way to do that is 3 x 2 = 6) So the denominator is 6. You need to shade is 1/2 since its 1/2 + 1/3. Now to make it easy change 1/3 into 2/6 and you can do that because its equivalent. So far 3/6 is shaded and now you add the 2/6 so it = 5/6
ANSWER 5/6 (Might be wrong...)
Time to write another big book again! No jk.
Anyways for the math test what I did was make 1/2 and and 1/3 equivelent fractions. What I mean by that is for them to have the same denominator. So what you do is turn 1/2 to 3/6 by multiplying the numerator and the denominator by 3. Then what you do is turn 1/3 to 2/6 so that now they have the same denominator. Now all you do is add 3/6 and 2/6 to get 5/6.
Another way is to turn 1/2 and 1/3 to decimals. So 1/2 turns to 0.5 and 1/3 turns to 0.3(repeating). Now all you got to do is add them up and you got 0.83(3 repeating) which is 5/6 as a decimal.
So in conclusion 1/2 + 1/3 does not equal 2/5 it equals 5/6.
Dam I think I wrote another book oh well.
for the test..
1/2 + 1/3 isnt 3/5 because.... its pretty obvious.. 1/2 > 2/5 and youre adding to 1/2, youre not subtracting.. a formula a figured out to find the answer (and all other unit fraction addition questions) was
N1 x (D1 + D2) = N of answer,
N2 x (D1 x D2) = D of answer.
for example ._.
1(n1)/3(d1) + 1(n2)/4(d2)
1(n1) x [(3d1)+(4d2)] = 7 n of answer
1(n2) x [(3d1)x(4d2)] = 12 d of answer
so 1/3 + 1/4 = 7/12
- if this doesn't make sense to you, im not changing it
Math Test:
1) i made both denominators the same by , mutiplying them together : 2 x 3 = 6. then i made that the new denominator.
2) I mutiplied the 1st fraction by denominator and numerator : 2 x 1 = 2. Then that becomes the new nominator for the new fraction.
3)I did the same to the other fraction : numerator x denominator = 3 . And now that becomes the other new numerator for the other new fraction.
4) now i put it all together : 2/6 + 3/6 = 5/6
kind of hard to explain on the computer but thats what i did and the answer that i got was 5/6!
The patterns that i saw are:
1/2 of 24 = 12
1/4 of 24 = 6
1/4 is the double of 1/2
12 is also the double of 6
This also works for:
1/4 of 24 = 6
1/8 of 24 = 3
1/4 of 12 = 3
1/2 of 6 = 3
1/4 is the half of 1/2 and 12 is the half of 6.
Math Test*
For the math test i first proved that 1/2 + 1/3 did not equal 2/5 by actually adding them together.
To add them together you need to make the denominators the same, you do that by finding the lowest common multiple of the two denominators ( 2 and 3 ). An easy way to do that is to multiply 2 and 3 together (this wont work for EVERY single question like this but it does for this one). So if we did that then we have 6 as our denominator but whatever we do to the denominator we need to do to the numerator. example
1 1 1x3 1x2 3 2 5
_ + _ = ___ + ___ = _ + _= _
2 3 2x3 3x2 6 6 6
Then i showed it as a decimal to prove that it wouldnt equal 2/5.
By dividing numerator by denominator. _
1/2 = 0.5 1/3 = 0.3 __
add those together you get 0.833
2/5 = 0.4 so it cant be the answer to 1/2+1/3
and third i drew some diagrams to show the difference if you put them together.
Patterns*
1. i noticed that 1/2 of 24 was 12 and 1/4 of 24 was 6 so i figured that it was just going down by a half of the number everytime the denominator doubled.
2. the three answers with three have a higher denominator as the number that its out of gets smaller.
example* 1/2 of 6
1/4 of 12
1/8 of 24
so . . . as the denominator doubles, so does the number causing the answer to stay the same.
3. And 1/4 of 12 is 3, so is 1/2 of 6. the differance in the numbers that your dealing with is just half so if you multiply them by 2 then they will be the same thing or if you divide it will all be equal and equivalent.
sorry if this became a book. o_o
hello again I WONDER why my post never shows up! . -.-
anywho. ;; the link i gave you was worng here it is http://i233.photobucket.com/albums/ee4/jasminerose_math/math.jpg
there you go it matches my answer on the 5th post! =]
I noticed that the denominator of the fraction in which you are trying to find out the fraction of's gets doubled, but the opposite happens to the answer to the right.
Another thing i noticed was that the equation 1/4 of 24 = 6 had an answer double that of 1/4 of 12 = 3 because the number in which you are trying to find a fraction of gets halfed and the opposite happens to the answer.
teh las' patt-arn i no-teeced was teh denominator of teh fractions get doubled, an' wen tis hapans, teh answer is shrunked by half ash well.
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