Question

One – half of a number is one – fourth. How do you find the number?

Answer 1

Hint: Assume the required number as x. Take half of this variable by multiplying it with \[\dfrac{1}{2}\] and equate the obtained product with \[\dfrac{1}{4}\]. Form a linear equation in x and solve for its value by making the coefficient of x equal to 1, to get the answer.

Complete step by step answer:
Here, we have been provided with the information that ‘one – half of a number is one – fourth’. We are asked to determine the number.
Now, let us assume the required number as x. First, we have to half this number. To do this, we have to multiply x with \[\left( \dfrac{1}{2} \right)\], so we get,
\[\Rightarrow x\times \dfrac{1}{2}=\dfrac{x}{2}\]
It is now said that this product is equal to one – fourth. That means we have to equate \[\dfrac{x}{2}\] with \[\dfrac{1}{4}\], so we have,
\[\Rightarrow \dfrac{x}{2}=\dfrac{1}{4}\]
Clearly, we can see that this is a linear equation in x. So, we need to solve this equation to get the value of x and our answer. To solve the equation means we have to make the coefficient of x equal to 1.
\[\because \dfrac{x}{2}=\dfrac{1}{4}\]
So, multiplying both the sides with 2, we get,
\[\Rightarrow 2\times \dfrac{x}{2}=2\times \dfrac{1}{4}\]
Cancelling the common factors on both the sides we have,
\[\Rightarrow x=\dfrac{1}{2}\]
Hence, the value of x is \[\dfrac{1}{2}\] which is the required number.

Note:
Here, we have obtained only one equation because we were asked to find the value of only one variable which we have assumed as x. You may check the obtained answer if it is correct or not. Take the product of the obtained value of x with \[\dfrac{1}{2}\] and if it is \[\dfrac{1}{4}\] then our answer is correct. You must know how to form a linear equation and must not get confused in the word play of question.