Question

If \[\dfrac{3}{2} \div \dfrac{1}{4} = n\] then \[n\] is between what number?

Answer 1

Hint: In this question, given that \[\dfrac{3}{2} \div \dfrac{1}{4} = n\]. First we need to find the value of \[n\] by solving the given expression. After finding the value of \[n\] , then we need to find n is between what numbers. First we need to solve the two given rational numbers. Rational numbers are the numbers which can be represented in the form of \[\dfrac{p}{q}\] where \[p\] and \[q\] are integers and \[q \neq 0\] . Mathematically, Rational numbers are denoted by Latin capital letter \[Q\] and also rational numbers are included in the real numbers.

Complete step by step solution:
Given,
\[\dfrac{3}{2} \div \dfrac{1}{4} = n\]
Here we need to solve this and need to find the value of \[n\].
By rewriting the given,
We get,
\[\Rightarrow \ n = \dfrac{\dfrac{3}{2}}{\dfrac{1}{4}}\]
On multiplying the numerator by the reciprocal of the denominator,
We get,
\[n = \dfrac{3}{2} \times \dfrac{4}{1}\]
On simplifying ,
We get, \[n = 3 \times 2\]
On multiplying,
We get,
\[n = 6\]
Now we need to find \[n = 6\] between what numbers.
We know that \[6\] lies between \[5\] and \[7\]
Thus we get \[n = 6\] lies between \[5\] and \[7\] .
If \[\dfrac{3}{2} \div \dfrac{1}{4} = n\] , \[n = 6\] lies between \[5\] and \[7\] .

Note:
Dividing by a fraction is nothing but multiplying by its reciprocal. Basically, rational numbers form a dense subset of the real numbers. We need to know that two different rational numbers may correspond to the same rational number. We can also find \[n\] between what numbers in the number line also. Number line is nothing but a graduated straight line used to represent the numbers in correct order.

Here it is clear that \[n=6\] lies between \[5\] and \[7\] .