What is $\dfrac{3}{4}$ divided by $\dfrac{4}{7}$ ?

Hint: In the given question, we are supposed to find the value of $\dfrac{3}{4}$ divided by $\dfrac{4}{7}$ . We start to solve the given question by dividing the fractions $\dfrac{3}{4}$ and $\dfrac{4}{7}$ . The division between the two will give us the required result.

Complete step-by-step solution:
We are asked to find the value of $\dfrac{3}{4}$ divided by $\dfrac{4}{7}$ . We will be solving the given question by finding out the result by dividing the two given fractions.
A fraction, in mathematics, represents a part of a whole thing. It consists of two parts namely,
numerator, denominator.
The number on the top is called the numerator.
The number on the bottom is called the denominator.
Let us understand the concept of the fraction with an example as follows,
Example:
$\Rightarrow \dfrac{a}{b}$
In the above fraction,
$a$ is the numerator of the fraction
$b$ is the denominator of the fraction
Example:
How do you divide $\dfrac{1}{2}$ by $\dfrac{1}{4}$ ?
We need to divide $\dfrac{1}{2}$ and $\dfrac{1}{4}$
$\Rightarrow \dfrac{\left( \dfrac{1}{2} \right)}{\left( \dfrac{1}{4} \right)}$
From the rules of arithmetic,
we know that $\dfrac{\left( \dfrac{a}{b} \right)}{\left( \dfrac{c}{d} \right)}$ can be also written as $\dfrac{a\times d}{b\times c}$
Here,
a = 1;
b = 2;
c = 1;
d = 4.
Writing the same, we get,
$\Rightarrow \dfrac{1\times 4}{2\times 1}$
Canceling the common factors, we get,
$\Rightarrow 2$
Now, we need to find the value of $\dfrac{3}{4}$ divided by $\dfrac{4}{7}$
Dividing the fraction $\dfrac{3}{4}$ by the fraction $\dfrac{4}{7}$ , we get,
$\Rightarrow \dfrac{\left( \dfrac{3}{4} \right)}{\left( \dfrac{4}{7} \right)}$
From the rules of arithmetic,
we know that $\dfrac{\left( \dfrac{a}{b} \right)}{\left( \dfrac{c}{d} \right)}$ can be also written as $\dfrac{a\times d}{b\times c}$
Here,
a = 3;
b = 4;
c = 4;
d = 7.
Writing the same, we get,
$\Rightarrow \dfrac{3\times 7}{4\times 4}$
According to the rules of fractions,
The multiplication of fractions is done by multiplying the numerators and denominators of the fraction, respectively.
Applying the same, we get,
$\Rightarrow \dfrac{21}{16}$
$\therefore$ The value of $\dfrac{3}{4}$ divided by $\dfrac{4}{7}$ is $\dfrac{21}{16}$.

Note: The result obtained in the given question can be cross-checked as follows,
The product of the result obtained and $\dfrac{4}{7}$ must result in $\dfrac{3}{4}$
From the above, the result obtained is $\dfrac{21}{16}$
Substituting the same, we get,
$\Rightarrow \dfrac{21}{16}\times \dfrac{4}{7}$
Canceling out the common factors, we get,
$\Rightarrow \dfrac{3}{4}$
The result obtained is correct.