Question

Represent \[ - \dfrac{7}{5}\] on the number line.

Answer 1

Hint:
The given rational number is an improper fraction. So, we will first convert it into a mixed fraction and check between which two integers it lies. Then we will divide the number line into the appropriate number of parts and mark the given rational number on the number line.

Complete Step by step Solution:
The given rational number is \[ - \dfrac{7}{5}\].
Since it is negative, it will lie on the left side of 0 on the number line.
Now, \[ - \dfrac{7}{5}\] is an improper fraction. So, to represent it on the number line, we will first convert it into a mixed fraction.
We see that \[ - \dfrac{7}{5} = - 1\dfrac{2}{5}\].
Here, \[ - 1\] is the whole part. So, \[ - \dfrac{7}{5}\] will lie between \[ - 1\] and the next integer which is \[ - 2\]. Thus, \[ - \dfrac{7}{5}\] lies between \[ - 1\] and \[ - 2\]. We will draw the number line as follows:

Since the denominator in \[ - \dfrac{7}{5}\] is 5, we will divide the space between \[ - 1\] and \[ - 2\] into 5 equal parts as follows:

Since \[ - \dfrac{7}{5} = - 1\dfrac{2}{5}\], we have to cross \[ - 1\] and mark \[\dfrac{2}{5}\] between \[ - 1\] and \[ - 2\]. Finally, we get:

Note:
We can also represent \[ - \dfrac{7}{5}\] by converting it into a decimal value.
We observe that \[ - \dfrac{7}{5} = - 1.4\], which lies between \[ - 1\] and \[ - 2\].
We can also write \[1.4\] as
 \[ - 1.4 = - 1 + 0.4 = - 1 + \dfrac{4}{{10}}\]
So, we can divide the space between \[ - 1\] and \[ - 2\] into 10 equal parts because the denominator in \[\dfrac{4}{{10}}\] is 10. The numerator is 4. Thus, we have to mark the 4th part in the 10 parts.