PPT: Proportional Reasoning-1 | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

 Page 1


PROPORTIONAL 
REASONING-1
Page 2


PROPORTIONAL 
REASONING-1
Observing Similarity in Change
Images can look similar even if sizes differ.
If both width and height change by the same factor, images remain similar.
If they do not change by the same factor, images look distorted.
Example -
Image A (60 × 40) and Image D (90 × 60) look similar ³ both scaled by factor 1.5.
Image B (40 × 20) looks stretched ³ not proportional.
Page 3


PROPORTIONAL 
REASONING-1
Observing Similarity in Change
Images can look similar even if sizes differ.
If both width and height change by the same factor, images remain similar.
If they do not change by the same factor, images look distorted.
Example -
Image A (60 × 40) and Image D (90 × 60) look similar ³ both scaled by factor 1.5.
Image B (40 × 20) looks stretched ³ not proportional.
R a t i o s
It is a comparison of two different things or numbers. We generally express the two numbers as a ratio using a colon (:). The colon is read 
as "is to"
Example -
The ratio of the number of notebooks to the number of pens is 3 : 6 .
3 notebooks is to 6 pens.
Page 4


PROPORTIONAL 
REASONING-1
Observing Similarity in Change
Images can look similar even if sizes differ.
If both width and height change by the same factor, images remain similar.
If they do not change by the same factor, images look distorted.
Example -
Image A (60 × 40) and Image D (90 × 60) look similar ³ both scaled by factor 1.5.
Image B (40 × 20) looks stretched ³ not proportional.
R a t i o s
It is a comparison of two different things or numbers. We generally express the two numbers as a ratio using a colon (:). The colon is read 
as "is to"
Example -
The ratio of the number of notebooks to the number of pens is 3 : 6 .
3 notebooks is to 6 pens.
Proportional Ratios
Ratios are proportional when the terms of these ratios change by the same factor.
For example, multiplying both terms of 60 : 
40 by ½:
60 × ½ : 40 × ½
= 30 : 20
This is the ratio of width to height in image C.
Similarly, multiplying both terms of 60 : 40 by 
1.5:
60 × 1.5 : 40 × 1.5
= 90 : 60
This is the ratio of width to height in image D.
Page 5


PROPORTIONAL 
REASONING-1
Observing Similarity in Change
Images can look similar even if sizes differ.
If both width and height change by the same factor, images remain similar.
If they do not change by the same factor, images look distorted.
Example -
Image A (60 × 40) and Image D (90 × 60) look similar ³ both scaled by factor 1.5.
Image B (40 × 20) looks stretched ³ not proportional.
R a t i o s
It is a comparison of two different things or numbers. We generally express the two numbers as a ratio using a colon (:). The colon is read 
as "is to"
Example -
The ratio of the number of notebooks to the number of pens is 3 : 6 .
3 notebooks is to 6 pens.
Proportional Ratios
Ratios are proportional when the terms of these ratios change by the same factor.
For example, multiplying both terms of 60 : 
40 by ½:
60 × ½ : 40 × ½
= 30 : 20
This is the ratio of width to height in image C.
Similarly, multiplying both terms of 60 : 40 by 
1.5:
60 × 1.5 : 40 × 1.5
= 90 : 60
This is the ratio of width to height in image D.
Ratios in their Simplest Form
We can reduce ratios to their simplest form by dividing the terms by their HCF (Highest Common Factor).
Image A
Ratio: 60 : 40
HCF of 60 and 40 is 20
Simplest form: 3 : 2
Image D
Ratio: 90 : 60
HCF of 90 and 60 is 30
Simplest form: 3 : 2
Image B
Ratio: 40 : 20
HCF of 40 and 20 is 20
Simplest form: 2 : 1
When two ratios are the same in their simplest forms, we say that the ratios are in p r o p o r t io n, or that the ratios are p r o p o r t io n a l. 
We use the '::' symbol to indicate that they are proportional.