Difference between revisions of "Ratio and Proportion"
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+ | ''[http://karnatakaeducation.org.in/KOER/index.php/ಅನುಪಾತ_ಮತ್ತು_ಸಮಾನುಪಾತ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div> | ||
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= Concept Map = | = Concept Map = | ||
− | + | [[File:Ratio .mm]] | |
__FORCETOC__ | __FORCETOC__ | ||
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===Learning objectives=== | ===Learning objectives=== | ||
===Notes for teachers=== | ===Notes for teachers=== | ||
− | For Solved Problems Click [http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion here] | + | For Solved Problems Click [http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion] |
+ | |||
+ | [[http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion here]] | ||
+ | |||
+ | [http://www.mathsisfun.com Maths is Fun] | ||
===Activity No # === | ===Activity No # === | ||
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* '''Evaluation (Questions for assessment of the child)''' | * '''Evaluation (Questions for assessment of the child)''' | ||
* '''Question Corner''' | * '''Question Corner''' | ||
+ | |||
+ | *'''How to make text bold''' | ||
+ | *''How to make text italic'' | ||
===Activity No # === | ===Activity No # === | ||
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= Hints for difficult problems = | = Hints for difficult problems = | ||
+ | ==Ratio and Proportionality= | ||
+ | ===Exercise 2.4.2=== | ||
+ | In the adjacent figure, two triangles are similar. Find the length of the missing side | ||
+ | This problem can be solved with the following steps. | ||
+ | #Prerequisites: students should know the concept of similarity and proportionality | ||
+ | *Proportionality : two ratios are equal then four quantities are in proportional | ||
+ | *Similar Triangles : If two triangles are said to be similar 1. if they are equiangular 2. the corresponding side are proportional | ||
+ | |||
+ | # Understanding/ analysing the given problem | ||
+ | ## Identifying/ Naming the triangles | ||
+ | ## Identifying the sides whose length is not given | ||
+ | ## comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa | ||
+ | ## should identify the corresponding sides (sides having same allignment) | ||
+ | # Procedure | ||
+ | ## find the ratio between the corresponding sides whose length is known <math>13 / 39 = 13 * 1 / 13 *3 = 1/3</math> | ||
+ | ## express proportional corresponding sides (using the property of similarity) | ||
+ | AC/DF = AB/DE | ||
+ | 13/39 = 5/x | ||
+ | 13 : 39 = 5 : x (use the property of proportionality i.e Product of extremes is equal to product of means) | ||
+ | 13 * x = 39 * 5 | ||
+ | x = 39* 5 /13 | ||
+ | |||
+ | Use the following Geogebra applet to understand proportion | ||
+ | |||
+ | <ggb_applet width="800" height="400" version="4.4" 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Latest revision as of 21:06, 17 May 2017
Philosophy of Mathematics |
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=Ratio and Proportionality
Exercise 2.4.2
In the adjacent figure, two triangles are similar. Find the length of the missing side This problem can be solved with the following steps.
- Prerequisites: students should know the concept of similarity and proportionality
*Proportionality : two ratios are equal then four quantities are in proportional
*Similar Triangles : If two triangles are said to be similar 1. if they are equiangular 2. the corresponding side are proportional
- Understanding/ analysing the given problem
- Identifying/ Naming the triangles
- Identifying the sides whose length is not given
- comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa
- should identify the corresponding sides (sides having same allignment)
- Procedure
- find the ratio between the corresponding sides whose length is known
- express proportional corresponding sides (using the property of similarity)
AC/DF = AB/DE
13/39 = 5/x 13 : 39 = 5 : x (use the property of proportionality i.e Product of extremes is equal to product of means) 13 * x = 39 * 5
x = 39* 5 /13
Use the following Geogebra applet to understand proportion
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