Question

Fill in the boxes with the correct symbol of and \[ > \],\[ < \],\[ = \].
\[\dfrac{{ - 4}}{3}\,\square \,\dfrac{{ - 5}}{7}\]

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Fractions are numerical values, these are part of the whole where whole is any number and fraction is a section or part of it.
There are two parts in a fraction numerator, the denominator.
Numerator: it is used to define how many part/s of the fraction are represented
Denominator: it is used to define in total how many parts are divides of whole
Any fraction is represented as: \[\dfrac{{Numerator}}{{Denominator}}\]

Complete step-by-step solution:
Here we are given two fractions \[\dfrac{{ - 4}}{3}\,,\dfrac{{ - 5}}{7}\]
\[ \dfrac{{ - 4}}{3} \] is improper fraction so we convert it into a mixed fraction by following above-mentioned rules
So \[ \dfrac{{ - 4}}{3} \] becomes \[ - 1\dfrac{{ - 1}}{3}\]
Here we can clearly see that it integer part of the mixed fraction is \[ - 1\] so on the number line \[\dfrac{{ - 4}}{3}\] is represented after \[ - 1\] that is \[ - 1.3333\]
\[\dfrac{{ - 5}}{7}\] is a proper fraction so it is clearly greater than \[ - 1\] keeping in mind that \[0 > - 1\]and so on.
That is \[0.714\].
So,
\[\dfrac{{ - 4}}{3}\,\, < \,\,\,\dfrac{{ - 5}}{7}\]
Or
\[ - 1.333 < 0.714\]
Additional information
Proper fraction is a type of fraction in which the numerator is less than its denominator. for example
\[\dfrac{5}{7}\], \[\dfrac{7}{{10}}\]…
Improper fraction: Fraction in which the numerator is greater than or equal to its denominator, for example:
\[\dfrac{{15}}{7}\], \[\dfrac{{17}}{{10}}\]…
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 \[2\dfrac{1}{7}\]
Negative fraction: negative sign signifies that the fraction lies on the negative side of the number line.
And also when dealing with a negative number line keep in mind that \[0 > - 1\],\[ - 1 > - 2\] and so on.

Note: When dealing with a negative number line keep in mind that \[0 > - 1\],\[ - 1 > - 2\] and so on. If there is an improper fraction first convert it into a mixed fraction and then compare so that we can see where it will lie on the number line.