most definitely, especially if the divisor is a negative number
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Yes, certainly. A quotient is the result of division ( a divisor into a dividend). The remainder can be bigger than the quotient, but not bigger than the divisor. For example 130 divided by 20 =6 with remainder of 10. Here 6 is the quotient and remainder is 10, which is bigger than the quotient
Because if the remainder is bigger than the divisor, the quotient can be increased and that will reduce the remainder. You can keep doing as long as the remainder is larger than the divisor. You stop only when it becomes smaller.
If the divisor of the dividend is a fraction then the quotient is increased as for example 14 divided by 2 = 7 but 14 divided by 1/2 or 0.5 = 28
Dividend divided by divisor equals quotient
The divisor is 9. quotient x divisor + remainder = dividend ⇒ quotient x divisor = dividend - remainder ⇒ divisor = (dividend - remainder) ÷ quotient = (53 - 8) ÷ 5 = 45 ÷ 5 = 9