Question

What is four times the quotient of 3 and 4?

Answer 1

Hint: In the above question, we are given two numbers as 3 and 4. We have to find the multiple of four times the quotient of these two numbers 3 and 4. In order to approach the solution, first we have to find the quotient of the numbers 3 and 4, and after that we can multiply the obtained quotient to the multiple that is given four times i.e. 4.

Complete step by step answer:
Given numbers are \[3\] and \[4\]. First we have to find the quotient of these two numbers \[3\] and \[4\] , therefore the quotient can be written as,
\[ \Rightarrow 3 \div 4\]
That gives us the following rational number,
\[ \Rightarrow \dfrac{3}{4}\]

Now we have to find the multiple of four times of the quotient, that is \[\dfrac{3}{4}\]. Therefore, we can write the required multiple by multiplying the quotient \[\dfrac{3}{4}\] by \[4\]. Hence, the multiple of the above quotient \[\dfrac{3}{4}\] by the multiple \[4\] can be written as,
\[ \Rightarrow \dfrac{3}{4} \times 4\]

Now the above expression has a denominator equal to the multiple, since both are equal to \[4\]. Therefore the two \[4\] ‘s will cancel each other leaving us with the remaining numerator, that is \[3\].
\[ \Rightarrow 3\]
That is our required multiple.

Therefore, four times the quotient of \[3\] and \[4\] is \[3\].

Note: The part i.e. number or expression, which is to be divided, is called the dividend. Whereas the part which divides the dividend is called as the divisor. The obtained solution after the division is called the quotient. Sometimes, the divisor can not completely divide the dividend, when the dividend is not a multiple of the divisor. In that case, some parts remained after the division. That remaining part is known as the remainder.Mathematically,
\[ Dividend \div Divisor = Quotient + \operatorname{Re} mainder\]