Question

How do you write the simplest form given by \[\dfrac{13}{20}-\dfrac{2}{5}\]?

Answer 1

Hint: Here we will get a positive fraction as result because both of them are proper fractions numerator
Complete step by step answer:
The given equation is \[\dfrac{13}{20}-\dfrac{2}{5}\]
First we have to make sure that both the fractions are simplified. We will check this by calculating the GCF of both numerator and denominator. If the GCF is 1 then we can proceed if it is other than 1 we have to divide both numerator and denominator with GCF.
So we have calculate GCF(13,20) and GCF(2,5)
First GCF( 13,20) we will do it by prime factorization method.
13 itself is a prime number
\[20=2\times 2\times 5\]
So there is no common term in prime factorization of 13 and 20
So, GCF(13,20)=1
Now GCF(2,5)
Here both 2 and 5 are prime numbers so their GCF will be 1
So, we can conclude that both the fractions are in their simplest forms.
Now we have to make the denominator both the fractions the same. So we calculate LCM of both the denominators.
LCM(20,5)
\[\begin{align}
  & 5\left| \!{\underline {\,
  20,5 \,}} \right. \\
 & 2\left| \!{\underline {\,
  4,1 \,}} \right. \\
 & \left| \!{\underline {\,
  2,1 \,}} \right. \\
\end{align}\]
So the LCM be \[5\times 2\times 2\times 1=20\]
Now the fractions be written as
\[\Rightarrow \dfrac{13-8}{20}\]
Now we have to perform subtraction of numerators. Then we will get
\[\Rightarrow \dfrac{5}{20}\]
Now we have to simplify it as
\[\Rightarrow \dfrac{1}{4}\]

So the solution is \[\dfrac{13}{20}-\dfrac{2}{5}=\dfrac{1}{4}\]

Note: We can also do it by converting fractions as decimals and can also be done without calculating GCF. There are a lot of ways to do it. It is the simplest problem if we are able to solve it with correct technique.