Question

Represent the following rational numbers on the number line.
\[\dfrac{{ - 9}}{7}\]

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Before we discuss the question let us understand what a number line is, it is basically a visual representation of numbers on a straight line. This line extends infinitely on both sides, horizontally which is used to compare numbers placed at equal intervals.

Suppose we want to represent \[a\dfrac{x}{y}\] on the number line first, we will locate \[a\] then between \[a\] and its adjacent number we will divide the whole section into \[y\] equal parts,
Now we mark the \[{x^{th}}\]point and that point will be \[a\dfrac{x}{y}\]

Complete step-by-step solution:
Given fraction: \[\dfrac{{ - 9}}{7}\]
First converting it to a mixed fraction since its numerator is greater than the denominator.
First, we need to divide \[\dfrac{{ - 9}}{7}\]
We get,
Quotient: \[ - 1\]
Remainder: \[-2\]
Now by following the steps to convert improper fractions to mixed fractions:
Quotient becomes integer part in mixed fraction and remainder becomes numerator part in fraction of mixed fraction and denominator will be same as a given fraction.
So, or mixed fraction will be \[ - 1\dfrac{-2}{7}\]
Now to represent it on the number line we follow rules mentioned above in fraction on the number line
First, we will locate \[ - 1\]

Now between \[ - 1\] and it's adjacent \[ - 2\] divide the whole section into \[7\] equal parts.

Now mark the \[{2^{nd}}\] point and that point will be \[ - 1\dfrac{2}{7}\] or \[\dfrac{{ - 9}}{7}\]

Additional Information:
Improper fraction: Fraction in which the numerator is greater than or equal to the denominator is an improper fraction, for example:
\[\dfrac{{15}}{7}\]
Proper fraction is a type of fraction in which the numerator is less than its denominator. for example
\[\dfrac{5}{7}\], \[\dfrac{7}{{10}}\]…
Mixed fraction: it is a type of fraction in which there are two portions. One is the whole number or integer part and another is the fractional part, for example:
\[\dfrac{{15}}{7}\] can also be written as \[2\dfrac{1}{7}\]
So how do we convert improper fractions to mixed fractions?
Following are the steps to convert improper fractions to mixed fractions:
$\bullet$ Divide the numerator part of the fraction with the denominator part.
$\bullet$ In case of,\[\dfrac{{15}}{7}\] we get 2 as quotient and 1 as remainder
Now
$\bullet$ The quotient will be integer part in mixed fraction
$\bullet$ The remainder will be numerator in the fraction part of the mixed fraction
$\bullet$ The denominator will be the same as in the original fraction.
So mixed fraction becomes \[2\dfrac{1}{7}\]
Fraction on the number line

Note: When dividing a section into equal parts keep in mind that it is not necessary to divide it into exactly ten equal parts and then mark the point so while dividing follow rules written above in fraction on a number line.