Question

What is $\dfrac{3}{5}$ Divided by $\dfrac{1}{4}?$

Answer 1

Hint: We need to know the concepts of reciprocity and division of fractions. We need to note that any number multiplied by a fraction $\dfrac{a}{b}$ can be written as the same number divided by a fraction $\dfrac{b}{a}.$ Hence by taking the reciprocal of a fraction, we can change from multiplication to division. Using this, we convert the division of the two fractions into the multiplication of two fractions. Then we perform multiplication of the two numerators and denominators and represent the answer.

Complete step-by-step solution:
In order to solve this question, let us first represent the question in the form of an equation. We write the first term $\dfrac{3}{5}$ in the numerator and the second term $\dfrac{1}{4}$ in the denominator.
$\Rightarrow \dfrac{\dfrac{3}{5}}{\dfrac{1}{4}}$
We know that dividing by a fraction is the same as multiplication by its reciprocal. This is shown as follows:
$\Rightarrow a\div \dfrac{b}{c}=a\times \dfrac{c}{b}$
Using this we convert the division of fractions into multiplication of fractions and we can write the above equation as shown.
$\Rightarrow \dfrac{3}{5}\times \dfrac{4}{1}$
Taking a product of the fractions, by multiplying the numerators and denominators,
$\Rightarrow \dfrac{3\times 4}{5\times 1}$
Simplifying the numerator and denominator by multiplying the terms,
$\Rightarrow \dfrac{12}{5}$
We can even convert this to mixed fractions by dividing the two and representing it as shown,
$\Rightarrow 2\dfrac{2}{5}$
Hence, $\dfrac{3}{5}$ Divided by $\dfrac{1}{4}$ is $\dfrac{12}{5}$ or $2\dfrac{2}{5}.$

Note: It is important to know the basic concepts of conversion of fraction from improper to mixed and vice-versa. We need to know how to convert multiplication of fractions into division of fractions and vice versa. We do this in order to simplify our calculations to a great extent.