Question

How to write in simplest form given \[\dfrac{1}{3}-\dfrac{2}{9}\]?

Answer 1

Hint: We are asked to write the \[\dfrac{1}{3}-\dfrac{2}{9}\] in its simplest form. Simplest form means that we have to convert this into a fraction whose numerator and denominator will have no common factor. To do this we first have to calculate this expression, and if the numerator and denominator of the obtained number have a common factor, we will cancel it by dividing both numerators and denominator.

Complete step by step answer:
We are given the expression \[\dfrac{1}{3}-\dfrac{2}{9}\], and have to write it in its simplest form. For this we will first calculate this expression. We know about the subtraction of fractions.
The subtraction of fractions \[\dfrac{a}{b}-\dfrac{c}{d}\] is calculated as follows, \[\dfrac{ad-bc}{bd}\]
We are given the \[\dfrac{1}{3}-\dfrac{2}{9}\], so here \[a=1,b=3,c=2,d=9\]
So, \[\dfrac{1}{3}-\dfrac{2}{9}\] is calculated as, \[\dfrac{1\times 9-2\times 3}{3\times 9}\]
\[\Rightarrow \dfrac{9-6}{27}=\dfrac{3}{27}\]
Here the numerator is 3 and denominator is 27, we have to check whether they have a common factor,
Factors of 3 are 1 and 3 whereas factors of 27 are 1, 3 and 27. From this we can say that 3 and 27 have a common factor which is 3, so we have to divide both numerator and denominator by this factor to get the simplest form. By doing this we get,
\[\Rightarrow \dfrac{\dfrac{3}{3}}{\dfrac{27}{3}}=\dfrac{1}{9}\]

So, the simplest form of the given expression \[\dfrac{1}{3}-\dfrac{2}{9}\]is \[\dfrac{1}{9}\].

Note: In this case the numerator and denominator have only one common factor. If there are more than one common factors present, we have to take the largest common factor and divide numerator and denominator by this factor. To check whether an answer is correct or not, check if the numerator can be divided by denominator, if it’s not then the answer is correct.