answer to the plant problem

You might think that this is a simple subtraction problem: 1/2 - 1/3 = 1/6, but if you draw a picture, your answers don't match:

So which is right? Well, the picture shows just what happened, so it has to be right, and 1/3 of the plant's survived. What would the picture look like if the answer was 1/2 - 1/3? Well, it would look like this:

This second picture shows that the cat ate 1/3 of the plants, not 1/3 of the plants that were left after some got squashed.

Lori planted some seedlings. Her little brother was playing, and squashed half of the seedlings (they did not survive). Then, her cat ate 1/3 of the seedlings that were left. How many of her seedlings survived?

1/3 of the plants that were not squashed were eaten:

1/2 -(1/3 of 1/2) = 1/2 - (1/3)x(1/2)

Answer 2/6 = 1/3 of the plants survived

The eaten plants are 1/3 of 1/2 of the plants (the whole for 1/3 is 1/2 of the plants)

Lori planted some seedlings. Her little brother was playing, and squashed half of the seedlings (they did not survive). Then, her cat ate another 1/3 of the original plot of seedlings. How many of her seedlings survived?

1/3 of the total plants were eaten

1/2 - 1/3

Answer: 1/6 of the plants survived.

The eaten plants are 1/3 of the total plants (the whole for 1/3 is all of the plants)

It's a subtle change, but an important one: you are taking 1/3 of different things in the two problems: in the first problem, you are taking 1/3 of the seedlings that are left after 1/2 were squashed, and in the second problem you are taking 1/3 of the total number of seedlings.