Amount or Number; Fewer than or less than
Both of these pairs concern agreement with count or uncountable (also called noncount) nouns.
In English something that is uncountable is an amount. Money is one example. Yes, I know you can count dollars, pennies, and the government counts in millions and billions, but money itself is uncountable because it is a generalization. So we talk about amounts of money, such as a large amount of money.
Number is used with countable things. The number of coins in your pocket tells us how much money you have in your pocket. So money acts like luggage and homework as an uncountable. They describe a general category.
Uncountable: money, luggage, homework
Countable: coins, suitcases, assignments
Another thing to notice about amount and number is that they are often accompanied by the preposition of.
The amount of money you will need is $75.00.
The number of coins you will need is four.
Fewer (than) and (less) than also relate to countable and uncountable nouns. Despite the fact that grocery stores and discount stores have signs that say Less than 8 items in this aisle, the sign should read fewer than because if you can count them then the are fewer.
The less money I have, the more bills I seem to have.
I have fewer dollars for this week than last week.
Fewer and less are used in comparison, so they must agree with the nouns that are being compared.
I have less money than my wife.
I have fewer dollars than my wife.