Question

What should be added to $-\dfrac{1}{2}$ to obtain the nearest natural number.

Answer 1

Hint: Now we know that natural numbers start from 1 and are listed as 1, 2, 3, … Hence we can find the nearest natural number to $-\dfrac{1}{2}$ . Now let us say after adding x we get the nearest natural number. Hence the nearest natural number is $=-\dfrac{1}{2}+x$ . Hence we will solve this equation to find the value of x.

Complete step by step answer:
Now let us first understand the Natural numbers.
Natural numbers are numbers which start from 1 and are listed as 1, 2, 3, ….
Now if we add 0 to the list we get the list of whole numbers,
Hence the whole number is 0, 1, 2, ….
Now again if we add negative numbers to this list we will get the list of integers,
The list of integer are $............-3,-2,-1,0,1,2,3,.......$
Now we will make rational numbers.
To write rational numbers we will make use of fractions as rational numbers are numbers which can be written in the form of $\dfrac{p}{q}$ , where p and q are integers and $q\ne 0$ .
Hence we get all the numbers of the form $\dfrac{p}{q}$ with p and q as integers and $q\ne 0$ are rational numbers.
Now consider the rational number $-\dfrac{1}{2}$
Let us check the position of $-\dfrac{1}{2}$ on the number line.

Now we can see the closest natural number to $-\dfrac{1}{2}$ is 1.
Now let us say we need to add x to $-\dfrac{1}{2}$ so we get 1.
Hence we have $x+\left( -\dfrac{1}{2} \right)=1$
Now rearranging the terms we get,
$x=1+\dfrac{1}{2}$
Now let us take LCM, hence we get
$x=\dfrac{2+1}{2}=\dfrac{3}{2}$
Hence we get $x=\dfrac{3}{2}$

Hence we have to add $\dfrac{3}{2}$ to $-\dfrac{1}{2}$ so that we get \[1\]

Note: Note that the natural number starts from 1 and not from 0. Hence do not make a mistake by assuming the closest natural number is 0. Now also note that while rearranging if we take the negative term of LHS to RHS it becomes positive. Similarly if we are shifting a positive term it becomes negative. We can also solve this completely by number line as we know we move 3 places to the right from $-\dfrac{1}{2}$ to reach 1 and here each interval is of length $\dfrac{1}{2}$