求救-小學數題

marthana

媽媽買餅一盒，她自己吃了9個，把餘下 31個分給兩孩子。 哥哥佔 ？/8 盒餅，弟弟佔 ？/5 盒餅；問弟弟可分到多少個餅。   
    

CMMANDY

? 是 1 個同一的數字嗎? 題目好像有D怪喎   

kids626

marthana 寫道:
媽媽買餅一盒，她自己吃了9個，把餘下 31個分給兩孩子。 哥哥佔 ？/8 盒餅，弟弟佔 ？/5 盒餅；問弟弟可分到多少個餅。   
    

Elder Brother gets 15/40 = 3/8
Younger Brother gets 16/40 = 2/5

Younger Brother gets 16 cakes.

marthana

想問如何得知哥哥有15個餅，弟弟有 16個餅？

丸媽媽

marthana 寫道:
想問如何得知哥哥有15個餅，弟弟有 16個餅？

算式:
31/40 = 16/40+15/40
將16/40和15/40化最簡分
= 2/5和3/8

所以便知哥哥有15個餅，弟弟有16個餅

marthana

31/40 = 16/40+15/40
將16/40和15/40化最簡分
= 2/5和3/8
____________________________

16/40+15/40 的 16 和 15 是如何設定？

CMMANDY

我諗可能是推理, 因為哥哥+弟弟就一定是31 , 當配合?/8 & ?/5 時, 就要考小朋友, 點樣知道分子分母是除得盡, 加上符合31 個餅, 又學多樣知識, Thanks !

丸媽媽

16/40+15/40 的 16 和 15 是如何設定？

如果係中學生就可以用x,y做代數去解,但小學生可以試下列解釋方法 (不過我覺得題目最令人混淆是沒有說明用最平均方式去分,只是用分母值去分哪一份是哥哥,哪一份是弟弟 )

假設將31除2,得出:
31/2 = 15餘1
所以 31/40=15/40+15/40+1/40
15/40 = 3/8 (分母值8,所以哥哥有15塊)
餘下15/40+1/40 = 16/40 = 2/5 (分母值5,所以弟弟有16塊)

06yy

Ans:
哥哥佔 ？/8 盒餅，弟弟佔 ？/5 盒餅:
改寫為:哥哥佔 x/8 盒餅，弟弟佔 y/5 盒餅
通分母=哥哥佔5x/40 盒餅，弟弟佔 8y/40 盒餅
since, 5x+8y=31  (餘下 31個分給兩孩子)
so, x=3 and y=2
i.e. 哥哥有餅:5(3)=15
      弟弟有餅:8(2)=16

marthana 寫道:
媽媽買餅一盒，她自己吃了9個，把餘下 31個分給兩孩子。 哥哥佔 ？/8 盒餅，弟弟佔 ？/5 盒餅；問弟弟可分到多少個餅。   
    

NeoMom

This question is quite meanless as the answer is not by mathematical deduction, just by trial and error. What we can only do is the deduce to 5X+8Y=31. Then we need to try each no. for x and y to fulfill the equation. In mathematical sense, it is nonsense. If the equation became 1249X + 2547Y=9836 then how can we find the answer!

marthana

這題目是同事抄他女女的功課題回來問，這只是一題五年級的數題，但我也被它考起了!  但很多謝各媽媽的幫忙!
    

kids626

marthana 寫道:
31/40 = 16/40+15/40
將16/40和15/40化最簡分
= 2/5和3/8
____________________________

16/40+15/40 的 16 和 15 是如何設定？

Because Mother ate up 9 cakes out of the 40 cakes, leaving 31 cakes to share between the two boys......

Murrychan

因這是小學問題所以要用分數方法去考慮.首先要知一盒餅有幾多塊,總數是40塊,媽媽佔9塊,餘下31塊給哥哥和弟弟分,

哥哥佔 ？/8 盒餅，弟弟佔 ？/5 盒餅:
改寫為:哥哥佔 x/8 盒餅，弟弟佔 y/5 盒餅
通分母=哥哥佔5x/40 盒餅，弟弟佔 8y/40 盒餅
since, 5x+8y=31 (餘下 31個分給兩孩子)
if x=1, y=26/8 or 3又1/4/(是分數)
if x=2, y=21/8 or 2又5/8(是分數)
so, x=3 and y=2(是整數)
i.e. 哥哥有餅:5(3)=15
弟弟有餅:8(2)=16

06yy

marthana 寫道:
這題目是同事抄他女女的功課題回來問，這只是一題五年級的數題，但我也被它考起了!  但很多謝各媽媽的幫忙!
    

You are welcome!

agoodfox

看似很簡單，睇真 D ，如果係比小學生計就都幾複雜。

全盒餅是40塊，把餘下 的31塊分給哥哥和弟弟，已知他們兩人所佔的分母分別是8和5，那麼31應由5和8的倍數組成。孩子自己試下不同組合，會發覺只有一個可能：8X2+5X3=31 ----->16+15

所以一個得16塊，佔16/40= 2/5盒；另一個15塊，佔15/40= 3/8盒。弟弟應是2/5那一位，分得16塊。

有時很難用一條式過列出，需分幾個步驟解釋。


這條數幾有趣，我會考下囝囝。

eviepa

這題目根本不值一晒。

If the first ? not equals to the second ?, the question will have infinite answers.

Basic maths law: 2 variables, 1 questions -->  The equation cannot be solved.

這只能是數學上的一個反面教材。就算原意是想學生用 trial and error 的方法的話，起碼要指定 the first ? & the second ? 都是自然數才會符合數學的意義。

jessc

eviepa 寫道:
Basic maths law: 2 variables, 1 questions -->  The equation cannot be solved.

這只能是數學上的一個反面教材。就算原意是想學生用 trial and error 的方法的話，起碼要指定 the first ? & the second ? 都是自然數才會符合數學的意義。

trial and error係一個而家書本經常逃避唔教的方法。
其實這條題目仲可以咁睇。
假設哥哥、弟弟有x/8、y/5，那麼：
x/8+y/5+31/40 => 5x+8y=31
但其實還有以下隱藏方程：
7>x>=0, 4>y>=0
所以這條題目不會有infinite number of answers
[分物遊戲的規則是不會分不到反而要賠給別人]
反而條題目好似assume左這絛題目的分數是不容許繁分數存在，相信是出題者用了五年級學生的知識程度來出, 未有考慮題目的嚴謹性。

bbkingdombb

It seems like an Olympic Mathematics question at P4/5 level. This is a difficult question for ordinary primary students w/o any training.

Let's see the solution.
The total is 40. The sum of the two guy is 31.

Assuming ？are integers (otherwise infinite solutions).
One has mulitple of one-eighth of 40
(therefore multiple of 5);
another has mulitple of one-fifth of 40 (therefore multiple of 8).

If we need a number (a multiple of 8), which can be a multiple of 5 after substracting this number from 31, the 'last-digit' of this number must be '1' or '6'.

Then within 40, it must be 16 (the next one is 56). Unique solution. No other choice. Then the other one is 15.

Therefore, no need to use equation, no need to trail and error. Only use concepts of multiples and 'last-digit' are enough. Sometimes, students are trained to see mathematics as a 'technical' subject which require routine 'steps' to solve. Olympic Maths require more careful observation of the numbers and the relationhsip between numbers. I see it's a very good training for students. what do u think?

:

kids626

I agree.

pistachio

I think most people tackle primary maths problems in complicated ways, e.g. algebric equations.

This question was intentionally made that the mother took 9 (3x3) pcs and the whole can contains 40 (8x5) pcs. And the core part was "integral". It's easy to imagine (just draw a picture to see) all the biscuits are placed in 5 rows each 8 pcs. As we know one brother takes multiple of 5 and if we combine them with the mothers, we can certainly get multiple of 8, i.e. 5n + 3x3=8m, which matches another brother's. Then, we can easily divide the biscuits into integral parts.

cheers