Question

Is it true that dividend over divisor = quotient + remainder ?

Answer 1

Hint: In this question, we need to state whether the given statement is true or not. The given statement is dividend over divisor = quotient + remainder. Here over stands for division . Division is nothing but an operation used in mathematics to divide a number by another number . In division, commonly there are four frequently used significant terms . They are dividend, divisor, remainder and quotient. At first we need to know the clear definition of those terms. To state whether the given statement is true or false, we can consider a simple example for division and from the result of the example, we can say whether the given statement is true or not .
Formula of the division :
$$\text{Dividend}÷\text{ Divisor}=\text{ Quotient}$$

Complete step by step answer:
Definition :
Division : Division is nothing but splitting large groups into equal smaller groups. Division means dividing a number by another number to get a new number which is the result.
Dividend : A number which is getting divided in the division is known as dividend.
Divisor : The number which divides another number is known as divisor.
Quotient : A number that we get as a result is known as the quotient.
Remainder : when a divisor which does not divide the given number completely , there exists a number which is known as the remainder.
Given statement ,
Dividend over divisor = quotient + remainder.
Here over stands for multiplication.
$$\text{Dividend}÷\text{ divisor}=\text{ quotient}+\text{ remainder}$$
This statement is not true. Let us explain this with an example. If $$37$$ is divided by $$8$$ .
By dividing we get the quotient as $$4$$ and the remainder as $$5$$ .
We can check by substituting the known values in the statement given.
$$\text{Dividend}÷\text{ divisor}=\text{ quotient}+\text{ remainder}$$
$$\Rightarrow 37÷8=4+5$$
Which is false.
Thus the given statement is not true.
Final answer :
It is not true that dividend over divisor = quotient + remainder

Note:
The concept used in this problem is terms of division. The correct statement is dividend is divisor over quotient plus remainder.
$$\text{Dividend }=\text{Divisor}\times \text{Quotient}+\text{ Remainder}$$
To verify this statement let us consider the dividend to be $$7$$ and the divisor to be $$3$$ .
We can check by substituting the known values in the statement
$$\Rightarrow 7=3\times 2+1$$
Thus this statement is true.