Question

The number $4$ is reduced by $\dfrac{1}{3}$ , what does this mean?

Answer 1

Hint:Here we have to tell what is the meaning of the statement given and find our answer accordingly. Firstly as we have been given that a number is reduced by another number if both the numbers are integer than this statement means that we have to subtract the two numbers. But as one number is integer and another is in fraction we can solve it in two ways by subtracting the integer number by a fraction part of the integer number.

Complete step by step answer:
We have been given that a number $4$ is reduced by $\dfrac{1}{3}$. As the statement is not clear we have two possible outcomes for it.Firstly we will simplify subtract $\dfrac{1}{3}$ by $4$ as reduction simply means subtraction as follows:
$\Rightarrow 4-\dfrac{1}{3}$
Taking LCM as follows:
$\Rightarrow \dfrac{4\times 3-1}{3}$
$\Rightarrow \dfrac{12-1}{3}$
So we get the answer as,
$\Rightarrow \dfrac{11}{3}$

Next we can say that the number $4$is reduced by $\dfrac{1}{3}$ of its value which can be written as follows:
$\Rightarrow 4-\left( \dfrac{1}{3}\times 4 \right)$
$\Rightarrow 4-\dfrac{4}{3}$
Taking LCM as follows:
$\Rightarrow \dfrac{4\times 3-4}{3}$
$\Rightarrow \dfrac{12-4}{3}$
So we get the answer as,
$\therefore \dfrac{8}{3}$
So we got two answers as $\dfrac{11}{3}$ and $\dfrac{8}{3}$.

Hence there are two possible outcome of the statement a number $4$ is reduced by $\dfrac{1}{3}$ that are $\dfrac{11}{3}$ and $\dfrac{8}{3}$.

Note:To reduce one number by another number generally means subtraction. We subtract the first number by the second number. But in this case our second number is a fraction and it is not clear whether we have to subtract the fraction from the number or we have to subtract that fraction part of the number from the number. So we have solved both the possibilities and got two answers.