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primary 6 | Maths
| Ratio
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Hi can help please
Date Posted: 4 years ago
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Date Posted:
4 years ago
A much easier and faster way :
(More suitable for PSLE. This question is very similar to the 'total unchanged question' you would have learnt, where you use ratios to solve)
Firstly,
X is 2/7 of (Y + Z). This tells you that the ratio of X : (Y + Z) = 2 : 7
Total of X,Y,Z = 2 units + 7 units
= 9 units
So ratio of X : (Y + Z) : (X + Y + Z)
= 2 : 7 : 9 ①
Next,
Y is 3/8 of (X + Z) This tells you that the ratio of Y : (X + Z) = 3 : 8
Total of X,Y,Z = 3 units + 8 units
= 11 units
So ratio of Y : (X + Z) : (X + Y + Z)
= 3 : 8 : 11 ②
Now since the total is the same so we make the units same.
Common multiple of 9 and 11 is 99
(9 x 11, 11 x 9)
Multiply the ratio in ① by 11,
ratio of X : (Y + Z) : (X + Y + Z)
= 22 : 77 : 99
Multiply the ratio in ② by 9,
ratio of Y : (X + Z) : (X + Y + Z)
= 27 : 72 : 99
From these 2 ratios you can see that X is 22 units and Y is 27 units.
So Z = 72 units - 22 units = 50 units
(Or 77 units - 27 units = 50 units)
(Or 99 units - 27 units - 22 units = 50 units)
So
a) X : Y : Z = 22 : 27 : 50
b) Z : (X + Y)
= 50 : (99 - 50)
= 50 : 49
(You can also find X+Y by adding 22 and 27)
(More suitable for PSLE. This question is very similar to the 'total unchanged question' you would have learnt, where you use ratios to solve)
Firstly,
X is 2/7 of (Y + Z). This tells you that the ratio of X : (Y + Z) = 2 : 7
Total of X,Y,Z = 2 units + 7 units
= 9 units
So ratio of X : (Y + Z) : (X + Y + Z)
= 2 : 7 : 9 ①
Next,
Y is 3/8 of (X + Z) This tells you that the ratio of Y : (X + Z) = 3 : 8
Total of X,Y,Z = 3 units + 8 units
= 11 units
So ratio of Y : (X + Z) : (X + Y + Z)
= 3 : 8 : 11 ②
Now since the total is the same so we make the units same.
Common multiple of 9 and 11 is 99
(9 x 11, 11 x 9)
Multiply the ratio in ① by 11,
ratio of X : (Y + Z) : (X + Y + Z)
= 22 : 77 : 99
Multiply the ratio in ② by 9,
ratio of Y : (X + Z) : (X + Y + Z)
= 27 : 72 : 99
From these 2 ratios you can see that X is 22 units and Y is 27 units.
So Z = 72 units - 22 units = 50 units
(Or 77 units - 27 units = 50 units)
(Or 99 units - 27 units - 22 units = 50 units)
So
a) X : Y : Z = 22 : 27 : 50
b) Z : (X + Y)
= 50 : (99 - 50)
= 50 : 49
(You can also find X+Y by adding 22 and 27)
Do take note that the ratios are expressed in whole numbers for PSLE
That indeed looks easier to understand for a PSLE student. However I still recommend my solution as it is more straight forward, even though it is longer. PSLE students should also be familiar with the simultaneous equations concept.
On the contrary, most students I've taught and come across dislike this method the most. If you look around the questions being posted here you'll see a lot of requests for non-algebra solutions.
Simultaneous equations are taught as 'units and parts' to them nowadays, supplemented by model drawing, avoiding the use of X and Y as variables. (Algebra is taught but only very basically, and mainly involves number operations)
Another problem arises when there are too many fractions in addition to having to manipulate the equations. It further confuses them. (It's a trend that most students struggle with Fractions). Students at that level are used to visualising fractions in terms of units. They are also not used to 'bringing over the terms to the other side' for equations.
What is considered straightforward to adults is actually tough for them since their cognitive abilities are not as developed yet. In my experience, school students have trouble with these, let alone P6 students.
Simultaneous equations are taught as 'units and parts' to them nowadays, supplemented by model drawing, avoiding the use of X and Y as variables. (Algebra is taught but only very basically, and mainly involves number operations)
Another problem arises when there are too many fractions in addition to having to manipulate the equations. It further confuses them. (It's a trend that most students struggle with Fractions). Students at that level are used to visualising fractions in terms of units. They are also not used to 'bringing over the terms to the other side' for equations.
What is considered straightforward to adults is actually tough for them since their cognitive abilities are not as developed yet. In my experience, school students have trouble with these, let alone P6 students.
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