Direct and inverse proportionality are two types of relationships between two quantities. When two quantities are directly proportional, it means that as one quantity increases, the other quantity also increases by the same factor. On the other hand, when two quantities are inversely proportional, it means that as one quantity increases, the other quantity decreases by the same factor.

Let's take an example to understand this better. Suppose you are making lemonade and you need to mix water and lemon juice in the correct proportions. If you add more water, the lemonade will become weaker, and if you add more lemon juice, the lemonade will become stronger.

If the amount of lemon juice you use stays constant, but you add more water, then the proportion of lemon juice to water will decrease. This is an example of inverse proportionality. As the amount of water increases, the proportion of lemon juice decreases.

On the other hand, if you keep the total volume of the lemonade constant, but add more lemon juice, then the proportion of lemon juice to water will increase. This is an example of direct proportionality. As the amount of lemon juice increases, the proportion of lemon juice to water increases as well.

In summary, direct proportionality means that two quantities change in the same direction, while inverse proportionality means that two quantities change in opposite directions.