Question

How do you write your answer in simplest form given\[\dfrac{7}{{12}} \div \dfrac{2}{9}\]?

Answer 1

Hint:For this kind of question you need to be clear that any fraction obtained in simplest form means after simplifying the fraction you won’t get any highest common factor except one, for further simplification, and once you reached at that level of simplified answer then you got your final simplified fraction you are looking for.

Complete step by step solution:
The given expression is \[\dfrac{7}{{12}} \div \dfrac{2}{9}\]

Here we will first see that each fraction given have any common factor to solve further or not, on finding factors for each fraction we get:
\[
\Rightarrow for\,\dfrac{7}{{12}}\,highest\,common\,factor\,is\,1 \\
\Rightarrow for\,\dfrac{2}{9}\,highest\,common\,factor\,is\,1 \\
\]
Here we get that the highest common factor for each fraction is one, and hence no further simplification can be done in each given fraction.

Now solving both fractions together we get:
\[
\Rightarrow \dfrac{{\dfrac{7}{{12}}}}{{\dfrac{2}{9}}} = \dfrac{{7 \times 9}}{{12 \times 2}} \\
\Rightarrow on\,dividing\,by\,3\,we\,get \\
\Rightarrow \dfrac{{7 \times 3}}{{4 \times 2}}\, \\
\]
Now no further simplification can be done here, and the highest common factor of numerator and denominator is one now, so our required result is:

\[ \Rightarrow \dfrac{{21}}{8}\]

Additional Information: In dividing the term by the HCF of both terms you should take care that both the terms are being divided every time you use the division, and the final outcome of any fraction is the least fraction that can be obtained.

Note: The fraction terms are obtained when the last possible division without making to decimal is completed, now the lowest fraction term can be written as in fraction or you can also write in decimal terms after reduction of the last smallest fraction, fraction can be of two types rational and irrational.