1. WELCOME
PRESENTATION

2. STD : 8th SUB: MATHEMATICS PRESENTATION BY MR.MAHADIK r.D.
k.k.ghule vidyalaya
manjari bk
SUB: MATHEMATICS
STD : 8th

3. Observe the following tables
Number of pens
Rupees 1 5 25 10 50 12 60 15 75 20
100
Distance (Km)
Time Taken (hours)
100
10 hours 50
5 hours 40
4 hours 30
3 hours 20
2 hours 10
1 hour

4. What you can conclude from the tables

5. Yes (1) one quantity increases the other also increases
Yes (1) one quantity increases the other also increases. (2) one quantity decreases the other also decreases This is the comparison of two quantities . It is also called variation or proportion. In above examples the quantities are said to be in direct variation( proportion ) with each other because the ratio of two quantities is constant e.g. In first table
No,.of pens 1 5 10 12 15
Price 25 50 60 75
Ratio
1/5

6. In second table
Distance (Km)
100 50 40 30 20 10
Time (hours) 5 4 3 2 1
Ratio
Direct Variation : If the ratio of two quantities remains constant they are said to be in direct variation with each other or directly proportional to each other.
If ‘p’ is in direct variation with ‘q’ then mathematically it is written as p α q where ‘α’ is called sign of proportionality.

7. Now p α q . ' p = k x q where ‘k’ is called constant of proportionality p/q= k This equation is called equation of variation.

8. Illustrative Example. The quantity ‘m’ directly varies with ‘n’
Illustrative Example * The quantity ‘m’ directly varies with ‘n’. When m=12, n=3 find k & write equation of variation . Solution : ‘m’ directly varies with ‘n’ ‘. m α n ‘. m=k x n ( k is constant) ‘. m/n=k ‘. 12/3=k ‘. 4=k The equation of variation is m/n= i.e. m=4 x n