Question

Fill in the blank
If a whole number ‘a’ is divided by a non – zero whole number b such that quotient is q then the remainder is _____ .

Answer 1

Hint: To solve this question, we will just use the property of division of the whole number by non – zero whole number for better understanding and also using the meaning of quotient, dividend, divisor and remainder, we will find the value of remainder in terms of a, b and q.

Complete step by step answer:
Before we solve this question, let us see what are whole numbers, why in question a number is divided by non – zero whole numbers and what are quotient, dividend, divisor and remainder.
The whole numbers are also called the positive integers or non – negative integers, if zero is included.
That is, the set W = { 0, 1, 2, 3, ……. } simply the whole number is a set of numbers including all natural numbers and zero too. For example, 67 and 89 are the whole number but 9.76 and $\sqrt{7}$ are not the whole number.
Now, any number is only divided by non – zero whole numbers because, in the world of mathematics anything divided by 0 is not defined.
Number which we divide is called dividend, the number which divides dividend is called divisor, the number which we get as result is quotient. The divisor which doesn’t divide a number completely produces a number known as remainder.
For example, we divide 6 by 2, we get 3. So, dividend = 6, divisor = 2 and quotient = 3 and remainder=0
We divide 7 by 2, we get 3 as quotient but remainder as 1 as quotient and remainder in case of whole number dividend and divisor, are also whole numbers.
As, we know $\text{Number = Quotient }\!\!\times\!\!\text{ Divisor + Remainder}$
In case, of question, number is a, quotient is q and divisor is b
So, $\text{a = q }\!\!\times\!\!\text{ b + Remainder}$
Or, $\text{Remainder = a - q }\!\!\times\!\!\text{ b }$, as a, q and b are whole numbers then remainder will also be whole numbers.
So, we will just write a – bq in blank.

Note:
To solve such question must know the basics of whole number and the rule for division of whole number by non – zero whole number which is $\text{Number = Quotient }\!\!\times\!\!\text{ Divisor + Remainder}$. Also, mention the final statement at the end of the question.