A mathematical operation of subtracting a rational number from another rational number is called the subtraction of rational numbers.
Two rational numbers are connected by a negative sign (minus) in some cases and it expresses that we have to subtract a rational number from another. In mathematics, it is not possible to subtract any rational number from another rational number directly due to their special form. Hence, we must use a special procedure for finding the difference of them mathematically.
In order to do subtraction of the rational numbers, you must have knowledge on the following two mathematical concepts.
The difference of the rational numbers can be evaluated in three simple steps.
Evaluate $\dfrac{4}{3}-\dfrac{2}{5}$
In this example, a minus sign is displayed between the rational numbers $\dfrac{4}{3}$ and $\dfrac{2}{5}$. It expresses that we have to subtract the rational number $\dfrac{2}{5}$ from another rational number $\dfrac{4}{3}$.
$3$ and $5$ are denominators and calculate the L.C.M for them. It is calculated that the least common multiple of them is $15$. Now, write it as the denominator.
$= \,\,\,$ $\dfrac{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}{15}$
Now, divide the lowest common multiple by each denominator of the rational number.
$(1). \,\,\,\,\,\,$ $\dfrac{15}{3} \,=\, 5$
$(2). \,\,\,\,\,\,$ $\dfrac{15}{5} \,=\, 3$
Now, multiply the quotient by the respective numerator of the rational number and write them in the numerator by connecting them by a minus sign.
$= \,\,\,$ $\dfrac{5 \times 4-3 \times 2}{15}$
Finally, simplify the expression in the numerator.
$= \,\,\,$ $\dfrac{20-6}{15}$
$\therefore \,\,\,$ $\dfrac{4}{3}-\dfrac{2}{5}$ $\,=\,$ $\dfrac{14}{15}$
In this way, the rational numbers are subtracted in the arithmetic mathematics.
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