Question

What is $\dfrac{1}{2}$ divided by $\dfrac{1}{3}$ $?$

Answer 1

Hint: To solve this question we need to have the knowledge of fraction and its properties. We should know to divide, multiply, add and subtract the fraction. In this question we also need to reciprocal the number for the purpose of calculation.

Complete step-by-step answer:
This question asks us to divide $\dfrac{1}{2}$ by $\dfrac{1}{3}$, mathematically it will be written as:
$= \dfrac{1}{2}\div \dfrac{1}{3}$
Important point while solving this question is that when a fraction is divided by another, the first step is to write the reciprocal of the second fraction which will be multiplied with the first fraction, as shown below. Doing this mathematically we get:
$= \dfrac{1}{2}\times \dfrac{3}{1}$
Multiplying the terms together in numerator and denominator respectively, we get:
$= \dfrac{1\times 3}{2\times 1}$
Thus the numerator becomes on $3$ and the denominator products to $2$.
$= \dfrac{3}{2}$
Now we will convert the above fraction and its decimal form. To do this we would multiply the numerator and denominator by $5$ so that denominator is $10$or is multiple of $10$
$= \dfrac{3\times 5}{2\times 5}$
On multiplying the numerator and denominator together.
$= \dfrac{15}{10}$
We will now remove $10$ and instead put the decimal in the number. On doing this we get:
$= 1.5$

$\therefore $ The value we get on dividing $\dfrac{1}{2}$ by $\dfrac{1}{3}$ in fraction form is $\dfrac{3}{2}$ and in decimal form is $1.5$.

Note: In most of the questions on fraction we need to reciprocal a fraction. Reciprocal means to change the numerator to denominator and vice versa. For instance reciprocal of $\dfrac{a}{b}$ becomes $\dfrac{b}{a}$.
We can check whether the solution is wrong or right. If $\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{p}{q}$ then the value of $\dfrac{a}{b}$ could be found by $\dfrac{a}{b}=\dfrac{p}{q}\times \dfrac{c}{d}$ . Now equating with the above question we get where $\dfrac{p}{q}$ is $\dfrac{3}{2}$ and $\dfrac{c}{d}$ is $\dfrac{1}{3}$ , thus on using the same formula we get
$= \dfrac{a}{b}=\dfrac{p}{q}\times \dfrac{c}{d}$
On putting the values:
$= \dfrac{a}{b}=\dfrac{3}{2}\times \dfrac{1}{3}$
$= \dfrac{a}{b}=\dfrac{1}{2}$
On further calculating we get,
$= \dfrac{a}{b}=\dfrac{1}{2}$
Thus the result we get on rechecking is the same as the question which is $\dfrac{1}{2}$ .