Question

Fill in the missing fraction: \[\square \, - \,\dfrac{3}{{21}}\, = \dfrac{5}{{21}}\]

Answer 1

Hint: To solve such questions, first take the unknown term at one side of the equal sign and known or constant terms on the other side. Then you should take the Least Common Multiple (L.C.M.) of the denominator. Since, here the denominator is the same, no need to take the L.C.M. and we can directly proceed to add the numerator.
Formula used: For any given fraction say, $\dfrac{a}{b}$and $\dfrac{c}{d}$ we find the addition or subtraction of the fraction as
$\dfrac{{ad\, \pm \,bc}}{{bc}}$ , where $bc$ is the Least Common Multiple.

Complete step-by-step solution:
First of all, we take all the known values on one side of the equal sign.
\[\square \, = \,\dfrac{5}{{21}}\, + \,\dfrac{3}{{21}}\,\]
Then, we see if the denominators are the same or different. Here, it is the same hence we do not have to take the L.C.M. We can directly add numerators.
\[
   \Rightarrow \,\square \, = \,\left( {\dfrac{{5 + 3}}{{21}}} \right)\, \\
   \Rightarrow \,\square \, = \,\left( {\dfrac{8}{{21}}} \right)\,\, \\
\]
So, the value of the missing part in the given question is \[\dfrac{8}{{21}}\]. This result can be checked by putting this value in missing part of the question and solving L.H.S. part. We get the same value as R.H.S. part.

Note: If the question contains fractions having different denominators, before adding the numerators first find the L.C.M. of the denominators. To find the L.C.M., we need to find the least numbers such that on multiplying with that to the denominators we get the both denominators to be the same. The value we obtain after multiplying that least number to the denominator is the L.C.M of the denominators. This is to keep in mind that those least numbers need not be equal to each other.