Q&A - PSLE Math

[ADoc]

Michaelia0816:

Ok now I need help! Pls help!

Question:
A) Mr Chan had a total of 160 pieces of $2 notes and $5 notes. He gave 50% of the $2 notes and 25% of the $5 notes to Susan and had 92 notes left.
a) Find the percentage of the number of $2 notes at first.
b) How much money did Mr Chan have at first?

Hi!
Let's look at the remainder and attempt to \"work backwards\":

gave away 50% of $2 notes --> left 50%
gave away 25% of $5 notes --> left 75%

=> 50% of $2 notes + 75% of $5 notes --> 92
that means 100% of $2 notes + 150% of $5 notes --> 92 x 2 = 184 } multiply by 2 throughout

qs says 100% $2 notes + 100% $5 notes --> 160
therefore if we compare (subtract) the two, we have 50% of $5 notes --> 184 - 160 = 24

=> 100% of $5 notes --> 24 x 2 = 48
=> 100% of $2 notes --> 160 - 48 = 112

(a) percentage of $2 notes of total number of notes = (112/160) x 100% = 70%

(b) amount of $5 notes = 48 x $5 = $240
amount of $2 notes = 112 x $2 = $224

total = $240 + $224 = $464

cheers
eugene

[again this is pseudo algebra (solving simultaneous by elimination method) in disguise but our primary kids are taught to solve such qs in this manner though not formally introduced to the concept until Sec1]

[PiggyLalala]

ADoc:

ADoc:

[quote=\"peggy\"]Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

Hi! Other than algebra, which some primary students may not be too comfortable with, we explain to them that before we can compare ratio or fraction units of the SAME qty, we must change them to the same number of units. This is an important concept in order to score those ratio qs, that I'm sure parents and students here are already very familiar with.

(2/3) x 3/3 = 6/9 } ali
(3/5) x 2/2 = 6/10 } raju

We see that Ali has 1 unit less than raju ---> 100 books
therefore Ali has 9 x 100 = 900 books.

Another variation of this sort of 2-mark qs is to ask for the fraction or ratio of say, Ali's to raju's.

cheers
eugene

Hi! My bad! tks for pointing out Zack. What i meant was 3/3 and 2/2 (as corrected above) to change to equivalent fractions. The concept is logically sound and in practice and can be construed as algebra in disguise in fact. It's just that most primary students prefer working in this manner to the ill-perceived horrors of algebra, especially cross multiplying and simultaneous linear eqn (which are not taught \"formally\" in most schools except by some primary teachers in certain schools that I know of).

cheers
eugene[/quote]No worries. We can understand your solution very well. And this is the way that the primary school kids are taught. In my opionion, we should not introduce the concept of algebra, like cross multiplication in Primary schools. Primary schools use units and parts or model method which is actually simple simple algebra that the kids can understand. Personally, I do not encourage solving primary school questions using simultaneous linear equations involving fractions and decimals, especially so for the weaker students. These methods are too complicated and there are always easier methods to solve such questions.

[Michaelia0816]

Pls help but this time method pls give me step by step answer

A shopkeeper had some apples and oranges. If 34 apples were sold, the ratio of the number of apples to number of oranges would be 3:1. If 85 oranges were sold, the ratio would be 29:4. How many apples did he have?

[Zack7]

MathIzzzFun:

Zack7:

[quote=\"ADoc\"]]Hi, my mind just isn't working. This should be an easy one but probably I might have solved too difficult questions lately till I can't solve the easy one. Please help.


2/3 of Ali's story books was the same as 3/5 of Raju's story books. If Ali had 100 fewer books, how many books would Ali have ?

Hi! Other than algebra, which some primary students may not be too comfortable with, we explain to them that before we can compare ratio or fraction units of the SAME qty, we must change them to the same number of units. This is an important concept in order to score those ratio qs, that I'm sure parents and students here are already very familiar with.

(2/3) x 3 = 6/9 } ali
(3/5) x 2 = 6/10 } raju

We see that Ali has 1 unit less than raju ---> 100 books
therefore Ali has 9 x 100 = 900 books.

Another variation of this sort of 2-mark qs is to ask for the fraction or ratio of say, Ali's to raju's.

cheers
eugene

your method is quite unorthodox i must say...

firstly, (2/3) x 3 = 2, not 6/9. same with 3/5

secondly, 6/9 is not 1 unit less than 6/10... in fact, 6/9 > 6/10. it might work as a shortcut in this question, but i don't think it is clear to the kids or even the right concept.

a clearer way would be

2/3 ali = 3/5 raja (as per the question)
ali = 9/10 raja (cross multiply)

now here comes the crucial step namely, how to interpret the above equation.
the equation tells you ali has only 9/10 as many books as raja.
always ask yourself when you are forming your conclusion, who has more books who has less. does it agree with the question? in this case, ali has less.

the equation might look like raja has fewer since there is a 9/10 factor, but this is not true because of the equal sign. it is important to note the equality sign.

so in this case, one should interpret it as : the WHOLE of ali is only EQUAL to 9/10 of raja. that means everything that ali has is not even equal to the whole of raja, but rather only equal to 9/10 of raja's books.

so this means 1/10 of raja's books is the amount that is more than ali. so ali has 100 books less than raja, which means raja has 100 more than ali.

9/10 of raja, which is = ali, is then 100x9 = 900.

hi Zack7,

if you were to go through the solution and understand the logic, you should see that it was just a typo omission by ADoc, the method is correct.

2/3 ali = 3/5 raja.. \"equalize\" the numerator ie 2/3 x 3/3, 3/5 x 2/2
we will get 6/9 Ali = 6/10 Raja --> So, Ali --> 9 units & Raja --> 10 units

.. this is a common method taught and it is easy to understand because one can easily draw a model to see that indeed Ali has 9 blocks and Raja has 10 blocks.

there will always be different approaches to solving a problem - no one method is better than the other.. it is a question of preference. One person may prefer the algebra approach, another may like the unit approach, while another will simply stick to model drawing. So, be open to various approaches because for some questions, the algebra approach is not the most efficient one.

cheers.[/quote]Now that you mention how models are used in conjunction with equalizing the numerator, it has become clear.

And I never claimed algebra is superior. Y do u see it that way? In fact I gave a solution which I thought was 'clearer' that contained no algebra.

Anyway, I must agree eugene's method is better now that isee how it works.

[Michaelia0816]

Hey need help with that question pls!

[Michaelia0816]

The apple question , pls give me step by step answer!!!

[Zack7]

Michaelia0816:

The apple question , pls give me step by step answer!!!!!

Would u prefer algebra or modeling?

Anyway by model

Notice that 4u + 85 = 1 u of the original orange

So 3u of the original apple is 12u + 255

So total original apple = 12u+ 255+ 34

Which is also the 29u of apple

So

12u + 289 = 29u
1u = 17
29 u = 493

U will have to draw out the model if you don't understand

3u | 34
1u

29u
4u| 85

[tianzhu]

Michaelia0816:

Pls help but this time method pls give me step by step answer

A shopkeeper had some apples and oranges. If 34 apples were sold, the ratio of the number of apples to number of oranges would be 3:1. If 85 oranges were sold, the ratio would be 29:4. How many apples did he have?

Hi

Hope this helps.

Best wishes.

http://farm6.staticflickr.com/5457/7049650203_fc7cc76d41_z.jpg\">

[Michaelia0816]

Dear everyone here, a question again cause my stupidness.

Sorry!
Father gave Nicholas and Rachel $630 to buy some clothes. Nicholas was given $60 more than Rachel. At the shop, Nicholas spent twice as much as Rachel. Rachel was left 3 times as much money as Nicholas. How many did Nicholas. How much did Nicholas spend ?

[Michaelia0816]

Thank you tianzhu !