Yes, because that is how remainder is defined. If the remainder was bigger, you would subtract one (or more) modular values until the remainder became smaller than the modulus.
The remainder must always be smaller.
It SHOULD always be less than the divisor... Otherwise your answer is wrong.
A clock is modular math. It has a base twelve. We use a base ten. If the clock had ten hours in a half day then the remainder when dividing would always be our answer.
Because if the remainder is greater, then you could "fit" another divisor value into it. if they are equal, then you can divide it easily. Thus, the remainder is always lower than the divisor.
The geometric mean, if it exists, is always less than or equal to the arithmetic mean. The two are equal only if all the numbers are the same.
Because if the remainder is greater, then you could "fit" another divisor value into it. if they are equal, then you can divide it easily. Thus, the remainder is always lower than the divisor.
Any pair of numbers will always form an arithmetic sequence.
Not always as for example 12/3 = 4 and no remainder but 13/3 = 4 with a remainder of 1
The sequence is arithmetic if the difference between every two consecutive terms is always the same.
The remainder is less than the divisor because if the remainder was greater than the divisor, you have the wrong quotient. In other words, you should increase your quotient until your remainder is less than your divisor!
Unless they are divided by themselves or one, they will always have a remainder.
The remainder is always 31 or less.