Question

Represent the fraction numbers on the number line.
 (i) \[\dfrac{7}{4}\]
 (ii) \[\dfrac{-5}{6}\]

Answer 1

Hint: The proper fraction is the part of the whole. So to represent the positive proper fraction, divide the scale from 0 to 1 in as many equal divisions as the number in the denominator and then the number in the numerator will be chosen from these parts, which will be the required representation in the number line.

Complete step by step answer:
(i) In this part we have to represent \[\dfrac{7}{4}\] in the number line.
Now, here we have the improper fraction, as the numerator is greater than the denominator. So we will convert this fraction in the mixed fraction, as shown below:
\[\begin{align}
  & \Rightarrow \dfrac{7}{4} \\
 & \Rightarrow 1\dfrac{3}{4} \\
\end{align}\]
Now, we have the 1 whole and \[\dfrac{3}{4}\] is the fraction part. We can also write the above mixed fraction as:
\[\Rightarrow 1\dfrac{3}{4}=1+\dfrac{3}{4}\]
So here we will have the fraction that is after 1 but between 1 and 2.
So now, in the number line we have to divide the number from 1 to 2 in 4 equal parts, as shown below:

Next, we will take the third division to represent \[\dfrac{3}{4}\], and hence the final representation is:

(ii) In this part we have to represent \[\dfrac{-5}{6}\] in the number line.
Now, here we have the negative proper fraction, as the numerator is less than the denominator. Also, this will lie on the negative side of the number line.
So now, in the negative side of the number line we have to divide the number from -1 to 0 in 6 equal parts, as shown below:

Next, we will take the fifth division to represent \[\dfrac{-5}{6}\], and hence the final representation is:

Note: Remember that the divisions made should have to be equal. The unequal division of the whole will not give the correct representation. Also, include the end point in the divisions made.