Question

What fraction on the number line below is in the wrong place?

A. $\dfrac{1}{4}$
B. $\dfrac{1}{8}$
C. $\dfrac{1}{2}$
D. $\dfrac{3}{4}$

Answer 1

Hint: First of all we will start with defining what a fraction is and then we will convert the fractions into decimal by dividing the numerator by the denominator and then compare them the smallest number will be on the left and so on. We will place them in ascending order and then we will compare it with the figure given in the question and get the answer.

Complete step-by-step answer:
First of all, we will understand what is a fraction? So a fraction is a number we need for measuring. For counting, we have the natural numbers: $1,2,3,4.....$ . But when we need to measure something for example, length, it will not always be a whole number. Therefore, we need numbers that are less than $1$ that means the numbers that are the parts of $1$ : half of $1$, a third , a fifth etc. In simpler terms, let’s take one-third for an example. It is represented as: $\dfrac{1}{3}$ , means 1 out of 3. The numerator of $\dfrac{1}{3}$ is $1$ and the denominator is $3$. They are called the terms of the fraction. The denominator shows the number of equal parts into which number $1$ has been divided. The numerator shows how many of those parts we selected. For example, in the example above: $\dfrac{1}{3}$, since the denominator is $3$, $1$ is divided into $3$ equal parts and we selected one part out of it as shown in figure below:

Now, to find which number is wrongly placed we will first convert the fraction into decimal and then write them in ascending order as the smaller number will lie on the left of the larger number.
Let’s convert one by one into the decimal form, for that we will just divide the numerator by denominator:
$\begin{align}
  & \Rightarrow \dfrac{1}{4}=0.25 \\
 & \Rightarrow \dfrac{1}{8}=0.125 \\
 & \Rightarrow \dfrac{1}{2}=0.5 \\
 & \Rightarrow \dfrac{3}{4}=0.75 \\
\end{align}$
Now we will arrange them in the ascending order : $0.125 < 0.25 < 0.5 <.75\Rightarrow \Rightarrow \dfrac{1}{8} < \dfrac{1}{4} < \dfrac{1}{2} < \dfrac{3}{4}$
As we see the ascending order the fractions will be placed in the same order on the number line as follows:

As we can see in the question figure: $\dfrac{1}{8}$ is in the wrong place.
Hence the correct option is B.

Note: Students can get confused while comparing the fractions as the fraction with larger denominator can be mistakenly taken as a higher number but it is not the case. If the numerators are the same then fractions with higher denominators are always smaller.