Multiplication and division are opposites, therefore by multiplying/dividing, you can use the other one to check your answer. say 2x2=4. if you didnt know that for sure (which you should,) you could go like 4/2=2. that means they are related
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the whole reason is this: multiplication is adding to that number in groups and division is subtracting from a number in groups.
For the specific case of whole numbers, you can consider multiplication to be repeated addition; and division to be repeated subtraction (see how often you can subtract something).
Decimal products are numbers that are the result of multiplication procedures and are not whole numbers. Decimal quotients are numbers that are the result of division procedures and are not whole numbers.
They are all numbers and obey the same rules for addition, subtraction, multiplication, division, exponentiation etc.
When it tells you to divide by a certain decimal it really will return an answer bigger than the number you started with because it is like multiplication.