Question

How do you divide $1\dfrac{1}{2}\div \dfrac{3}{4}$?

Answer 1

This question is from the topic of pre-algebra. In solving this question, we will first solve the term $1\dfrac{1}{2}$. We will convert this mixed fraction into an improper fraction. After that, we will divide that improper fraction by the term $\dfrac{3}{4}$. After solving further questions, we will get our answer. After that, we will see an alternate method to solve this question.

Complete step by step answer:
Let us solve this question.
In this question, we have asked to divide $1\dfrac{1}{2}\div \dfrac{3}{4}$. Or, we can say we have to solve the term $1\dfrac{1}{2}\div \dfrac{3}{4}$.
As we can see that the term $1\dfrac{1}{2}$ is a mixed fraction, then we will first convert this into a proper fraction. Here, the number 1 is a whole number part and $\dfrac{1}{2}$ is a fraction part. For converting, we will multiply the whole number with the denominator of the fractional part. After that, we will add the numerator with the multiplied number. We will write the resultant in the numerator and write the denominator as the same for improper fraction.
So, we can write the term $1\dfrac{1}{2}$ as
$1\dfrac{1}{2}=\dfrac{2\times 1+1}{2}=\dfrac{3}{2}$
Hence, we can say an improper fraction of the term $1\dfrac{1}{2}$ is $\dfrac{3}{2}$.
Now, let us solve the term $1\dfrac{1}{2}\div \dfrac{3}{4}$.
This term can also be written as
$1\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{3}{2}\div \dfrac{3}{4}$
The above equation can also be written as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{3}{2}\times \dfrac{4}{3}$
The above equation can also be written as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{4}{2}$
As we know that 4 divided by 2 is 2, so we can write the above equation as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=2$
Now, we have divided $1\dfrac{1}{2}\div \dfrac{3}{4}$ and have got the answer as 2.

Note:
As we can see that this question is from the topic of pre-algebra, so we should have a better knowledge in the topic of pre-algebra.
Let us solve this question by alternate method.
We can write the term $1\dfrac{1}{2}\div \dfrac{3}{4}$ as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\left( 1+\dfrac{1}{2} \right)\div \dfrac{3}{4}$
We can write 1 as $\dfrac{2}{2}$. So, we can write the above equation as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\left( \dfrac{2}{2}+\dfrac{1}{2} \right)\div \dfrac{3}{4}$
The above equation can also be written as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\left( \dfrac{2+1}{2} \right)\div \dfrac{3}{4}$
The above equation can also be written as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\left( \dfrac{3}{2} \right)\div \dfrac{3}{4}$
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{3}{2}\div \dfrac{3}{4}$
The equation can also be written as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{3}{2\times \dfrac{3}{4}}$
The above equation can also be written as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{1}{1\times \dfrac{1}{2}}$
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{1}{\dfrac{1}{2}}$
The above equation can also be written as
$\Rightarrow 1\dfrac{1}{2}\div \dfrac{3}{4}=2$
Hence, we have got the same answer. So, we can use this method too to solve this question.