When multiplying a fraction by a fraction why do you get a smaller fraction?

Fractions are just numbers. If you multiply a number by one, you get the same number. If you multiply a number by a number smaller than 1, you get a smaller number. If you multiply a number by a number bigger than one, you get a larger number. Dealing with fractions doesn't really tell you anything about the result of your operations.

1 = 1/1 = 2/2 = 50/50 = etc

.5 = 1/2 = 2/4 = 3/6 = etc

2 = 4/2 = 8/4 = 12/6

Fractions are just a form of representing a number. Sometimes they are simpler to visualize than long decimals, such as .555555555. But that decimal number is the same as 5/9, a nice and simple expression in fraction form. And you can usually multiply a fraction in your head, versus a decimal. What is .1818181818 * .25? Well its the same as 2/11 * 1/4 which is 2/44 or 1/22.

An example of a non-decreasing fraction multiply is:

1*2 = 1/1 * 2/1 = 2/1 = 2. 2 > 1, so this is a simple (and trivial) example of not getting a smaller fraction. You only get a smaller fraction when you multiply by values smaller than one. A fraction that is smaller than one is the denominator being larger than the numerator (1/2 or 12/28828 or whatever).

Hope this clears up any confusions!

Additional answer

If you substitute the Word 'of' for 'times' in the sentence 'what is 4 times 5?' then you get 'what is 4 of 5?' = 20. If you say 'what is half of eight' then it is obviously 4 (which is smaller), thus answering your question.