Question

how to differentiate between direct and inverse proportions explain with examples

Answer 1

In a direct proportion, as one of the quantities INCREASES the other also INCREASES.

In an inverse proportion, as one quantity INCREASES the other DECREASES.

Direct:
MORE boxes of cereal will cost MORE money.
MORE people will eat MORE food.
LESS money will buy FEWER sweets.
MORE clothes will need MORE suitcases.

Inverse:
A task shared by MORE people will take LESS time.
Travelling at a FAST speed will take LESS time for a journey.
If MORE people share a pizza. each person will get LESS.
MORE expensive price means FEWER items can be bought for the same amount of money.

Each type of proportion has a constant. (k)

In DIRECT proportion, find the constant by DIVIDING the matching quantities. (they are equivalent fractions:)

1827=1015=2436=5075=3857=23=k

In INVERSE proportion, find the constant by MULTIPLYING the matching quantities:

2×30=5×12=15×4=3×20=10×6=60=k

If you call the two quantities xandy, then we have:

Direct proportion: k=xy

Inverse proportion: x×y=k

Hope this helps.

Answer 2

in direct proportional both are like equivalent means as one value increases another also increases . for example F directly proportional to the differential of momentum.(refer newtons second law) .
  in inversly proportional as value of inversed quantity increases another decreases . if the inversed value decreases another quantity increases.
  for example acceleration is inversely proportional to mass. as the mass increases acceleration decrreases and if the mass decreases accelration of the body increases