WELCOME PRESENTATION

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

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

What you can conclude from the tables

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

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.

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.

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=4 i.e. m=4 x n