Question

How do write in the simplest form of a given fraction $\dfrac{7}{15}-\dfrac{2}{15}$?

Answer 1

Hint: Here we must perform the mathematical operation, subtraction between two given fractions. Since the denominators are the same, we can directly perform the mathematical operation on the numerator keeping the denominator the same. Now to write it in the simplest form, Write down the factors of the constants in numerator and denominator. Now cancel out the common factors. The factors which are left will be written as the solution for the simplest form.

Complete step by step solution:
The given expression is, $\dfrac{7}{15}-\dfrac{2}{15}$
Here we are performing the addition operation between two fractions, $\dfrac{7}{15},\dfrac{2}{15}$
If the denominators are the same for both the fractions we can directly add or perform any operations.
Since our denominators are the same which is $15\;$, we can directly perform the subtraction operation.
On evaluating the numerator part keeping the denominator as it is, we get,
$\Rightarrow \dfrac{7-2}{15}$
On subtracting the terms in the numerator, we get,
$\Rightarrow \dfrac{5}{15}$
Here in our question, we are asked to write in the simplest form of the expression.
So, we write down the factors for the integers in the numerator and the denominator.
$\Rightarrow \dfrac{1\times 5}{1\times 3\times 5}$
We can see that there are two common factors.
They are $1,5\;$ .
Since they are common in the numerator as well as the denominator, we can cancel them out.
After the simplification we get,
$\Rightarrow \dfrac{1}{3}$
Hence the simplest form given $\dfrac{7}{15}-\dfrac{2}{15}$ is $\dfrac{1}{3}$

Note: A fraction is in simplest form if the top and bottom have no common factors other than $1$ . You might also hear the simplest form called "lowest terms”. You can divide the numerator and denominator by their Greatest common factor (GCF). Whenever there are different denominators in a subtraction or addition or any other operation equation, the first step must be to convert it in such a way as to get the same denominators.