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Monday, July 24 2017 @ 09:45 AM CDT
 Forum Index >  Test Paper Related >  Primary 4 Matters
 Fraction again
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By: pearldyn (offline)  Thursday, April 08 2010 @ 07:46 PM CDT (Read 1400 times)  
pearldyn

Hi again!

Any takers on this one?

An MRT train was 2/5 full of passengers. At the first station, 1/2 of the passengers alighted
and 17 people boarded the train. The train is now 1/4 full. How many passengers were there
on the train at first?

This time, I want to try so you can see how I think and from there I want to improve on my thinking
skills which I am lacking off.

Ok........First I take 1/2 minus from 2/5 = 1/5 (is this correct?)
Then.....I have to take the 1/4 = 1/5 + 17 (is this correct too?)

After that........actually I dont know already. Ha!
The only thing I can think of is that this is a "working backwards" problem sum.

Okay, the answer given is 136.

Thank you!

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By: kohkah (offline)  Friday, April 09 2010 @ 02:11 AM CDT  
kohkah

1/4=5/20,
1/5=4/20
therefore, 1/20=17
at first, 2/5---->8/20
17*8=136

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By: thayal (offline)  Monday, April 12 2010 @ 09:49 AM CDT  
thayal

HI could anyone help me this fraction problem?

Judy had 68 ore stickers than Jenny. After Jenny gave away 1/4 of her stickers and Judy gave away 25stickers, Jenny had 2/3 as many stickers as Judy. Ho many sticker did Judy hav at first?

Are there any model drawigs books for this type of problem sums?Please let me know

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By: AVE (offline)  Tuesday, April 13 2010 @ 12:22 AM CDT  
AVE

Hi Thayal,
sure, here is my solution although a little bit of algebraic (I can only answer systematically using algebraic method):

Let x= the original number of stickers that Judy had
y = original number of stickers that Jenny have

1st sentence:Judy had 68 ore stickers than Jenny.
x = 68 + y

Jenny gave away 1/4 of her stickers:
y - 1/4y

Judy gave away 25stickers:
x-25

Jenny had 2/3 as many stickers as Judy:
y - 1/4y = 2/3 (x-25) manipulate this eq to get y:

3/4y = 2/3 (x-25)
y = 8/9 (x -25) ---> substitute to 1st eqn: x = 68 + y
x = 68 + 8/9 (x-25)
x = (68(9) + 8x -200)/9
9x = 612 + 8x -200
9x - 8x = 612 - 200
==================
x = 412 ---> answer
==================

check answer:
y = 412 -68 = 344

y - 1/4y = 2/3(x-25)
344 - 1/4(344) = 2/3 (412 -25)
258 = 258

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By: kohkah (offline)  Tuesday, April 13 2010 @ 01:44 AM CDT  
kohkah

Start drawing the model from the end of the question.

Jenny is 2/3 as many as Judy

Judy |------------------------------|------------------------------|------------------------------|
Jenny|--------------------|--------------------|-------------------|

Judy give away 25 and Jenny give away 1/4

Judy |------------------------------|------------------------------|------------------------------| 25|<----give away so we put it back
Jenny|--------------------|--------------------|-------------------| 1/4 |<----1/4 give away so we put it back

From here u can see 3/4 of Jenny equal to 2/3 of Judy, we have to refine the model, before that, we get the lowest common multiple of 2 and 3 which is 6


Redraw model


Judy |---------|---------|---------|---------|---------|---------|---------|---------|---------|---------|<---25--->|<---- give away 25 left 43, Judy is 68 more
Jenny|---------|---------|---------|---------|---------|---------|---------|XXXXX|XXXXX| <----XXXX denote 1/4 give away

From here we can see that 1 block of |---------| is equal to 43.
Judy has 9 blocks so it will be 43*9=387, plus the 25 she give away, it yield 412!

For questions with fractions in different denominator and numerator, it will require the student to refine the blocks into smaller sizes by obtaining the lowest common multiple.

Sorry for the model is badly done. :<


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By: pearldyn (offline)  Tuesday, April 13 2010 @ 09:19 AM CDT  
pearldyn

Quote by: kohkah

1/4=5/20,
1/5=4/20
therefore, 1/20=17
at first, 2/5---->8/20
17*8=136



kohkah,

why 1/20 = 17 ?

I thought 1/5 + 17 = I dont know what

oh dear, i am so stressed! I am sorry, I just didnt get it.

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By: kohkah (offline)  Wednesday, April 14 2010 @ 10:50 PM CDT  
kohkah

no worry,

lets do it slowly Wink

from the question you know 17 passengers boarded contribute a fraction to increase the capacity from 1/5 to 1/4 .

in model drawing, draw 2 same size of blocks, one divided into 5 parts the other 4 parts.

|-------------------|-------------------|-------------------|-------------------|-------------------| <---------------------> 5 blocks
|------------------------|------------------------|------------------------|------------------------| <---------------------> 4 blocks
--->|-----|<---------17 is here.

by obtaining the LCM of 4 and 5, which is 20, we are able to normalise/ convert the 1/5 and 1/4 into 4/20 and 5/20 respectively.
if memory serve me right, after obtaining the LCM, the students are to further divide the block into smaller size, subsequently they will be able to visual 1 block/unit of it is 17.

for non student, we get 1/4 - 1/5 = 1/20, from here we shall understand it is the 17 passengers that boarded the train.


For model involve fractions, students have to be able to get LCM, lowest common multiple, and resize the model into smaller units.





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