Question

How do write in simplest form given $\dfrac{7}{10}-\dfrac{2}{15}$ ?

Answer 1

Hint: Here in this question, we have to subtract two fractions. And the fractions are having different denominators so we need to find Least Common Multiple (LCM) first of both the denominators to make them common. Then, we have to subtract and write in simplest form. Simplest form is done by reducing the terms.

Complete step by step answer:
Now, let’s solve the question.
Like fractions are those which have the same denominators. Whereas unlike fractions are those fractions whose denominators are different and they can be converted to like fractions.
In order to convert unlike fractions to like fractions first we have to take Least Common Multiple (LCM) of the denominators whether the cases are of subtraction, addition, greater than or lesser than or ascending or descending. Only in multiplication or division, we don’t convert unlike fractions to like fractions.
After subtraction we have to write the final answer in simplest form or lowest form which means we have to reduce the numerator and denominator by dividing them with the least common multiple each time.
First, write the fraction given in the question.
$\Rightarrow \dfrac{7}{10}-\dfrac{2}{15}$
Now, find the LCM of denominators 10 and 15.
$\begin{align}
  & 2\left| \!{\underline {\,
  10,15 \,}} \right. \\
 & 3\left| \!{\underline {\,
  5,15 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5,5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,1 \,}} \right. \\
\end{align}$
LCM of 10 and 15 are: $2\times 3\times 5=30$.
Next step is that we have to divide the original denominators with the LCM i.e. 30 and the resulting number will be multiplied with the numerator. Let’s perform this step now.
$\Rightarrow \dfrac{21}{30}-\dfrac{4}{30}$
Now subtract:
$\Rightarrow \dfrac{17}{30}$
So this is our final answer.

Note: As you can see the final step, we haven’t reduced it to any simplest form. Because the answer is already in the reduced form. Major mistake which can be done is after taking LCM, numerators are copied directly from the original as they are: $\dfrac{7}{30}-\dfrac{2}{30}$like this. Please avoid such mistakes.