Multiplication asks the same question: 4 x 6 is not 4 times 6, the question being asked is what is the product of four groups of six ones. The answer again falls into our number system which indicates that this is two 10s and four oneswe call this result 24, too.
What then does 2/3 x 3/4 ask? It wants to know what 2/3 of 3/4 will produce. Think about your pay. The boss indicates that sales are slow and they can only give you 2/3 of your pay. Real happy, huh. I think not, because you realize that your pay will be divided into three parts and you will only get two of the parts. Why is that?
The reason is that 2/3 means to divide something into three equal parts and do something with two of the parts. It sure works for a pizza. If you divide the pizza into three equal parts and you are lucky to get two of the parts you get to eat 2/3 of the pizza. If it works for pizza, it has to work for everything.
Lets get back to the 2/3 X 3/4 problem.
What it means is as follows. 3/4 is to be divided into three parts and you are going to be able to keep two of the parts. If I divide 3/4 into 3 parts, each part will be 1/4. If I get to keep two of these parts, this will result in my having 2/4. If I write this in simplest terms, it means that I will get 1/2 of what ever we are talking about. 2/3 of 3/4 of a mile is 1/2 of a mile. 2/3 of 3/4 of a dollar is 1/2 a dollar or 50 cents. 2/3 of 3/4 of an hour is a half of an hour.