Question

How do you multiply rational numbers in fraction form?

Answer 1

Hint:The given question deals with the concept of rational number. Here, in this question we are asked how to multiply rational numbers in fractional form. Before understanding how to multiply rational numbers in fraction form, we first need to understand what rational numbers are.

Complete step by step answer:
A rational number is any number, be it natural number or integer, which can be written in the form of $\dfrac{p}{q}$ such that $q$ is never equal to zero. A rational number is said to be in a standard form if and only if it satisfies two conditions;
-The denominator should be an integer which is greater than zero.
-The only common divisor between numerator and denominator should be one.
Now, according to the question, when given two rational numbers, you can simply multiply the numerators and denominators and get the required answer. Such as,
$ \Rightarrow \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{{a \times c}}{{b \times d}}$
The above can easily be explained with a help of an example.

Let the two rational numbers be $\dfrac{5}{8}$ and $\dfrac{4}{7}$. Now, we multiply them,
$ \Rightarrow \dfrac{5}{8} \times \dfrac{4}{7} = \dfrac{{5 \times 4}}{{8 \times 7}} = \dfrac{{20}}{{56}}$
This can be further simplified, for doing so we can divide both numerator and denominator by $4$ because it is the greatest common divisor of the two numbers.
$ \Rightarrow \dfrac{{20}}{{56}} = \dfrac{5}{{14}}$
That’s how we multiply rational numbers in fractional form.

Note:The given question was very easy and basically theoretical. To explain better, we used an example. Students should know the concept of rational numbers for better clarity and understanding of complex rational number related questions. Students should also know about the properties of rational numbers.