Question

Subtract \[\dfrac{8}{10}from\dfrac{11}{25}\]

(a) \[\dfrac{18}{50}\]
(b) \[\dfrac{-9}{25}\]
(c) \[\dfrac{25}{9}\]
(d) \[\dfrac{50}{18}\]

Answer 1

Hint: Firstly, we will check whether any of the fractions is simplified or not.

Complete step-by-step answer:
We can see that the fraction \[\dfrac{8}{10}\] has a common factor, i.e. 2. So we will simplify the fraction. After simplifying the fraction, we get \[\dfrac{4}{5}\] . Now, we need to make the denominators of these two fractions the same. We will calculate the L.C.M. of the two fractions - \[\dfrac{4}{5}\ and\ \dfrac{11}{25}\] .for this. And after calculating their L.C.M., we will make their denominators the same by multiplying them with suitable numbers. After doing so, we will subtract \[\dfrac{4}{5}from\dfrac{11}{25}\].

As mentioned in the hint, we will make the denominator of both the fractions. As we know that the L.C.M. of 5 and 25 is 25, so we will make their denominators 25 by multiplying them by suitable numbers.

\[\begin{align}
  & \dfrac{4\times 5}{5\times 5}=\dfrac{20}{25} \\
 & \dfrac{11\times 1}{25\times 1}=\dfrac{11}{25} \\
\end{align}\]

When we multiply or divide the denominator by any number, we also need to multiply or divide the same number by the numerator also.

Now, as we have made the denominators of the two fractions same, we will subtract
\[\dfrac{20}{25}from\dfrac{11}{25}\]

On doing the above, we get following

\[\dfrac{11}{25}-\dfrac{20}{25}=\dfrac{-9}{25}\]

And hence, the answer of this question is (b) \[\dfrac{-9}{25}\].

Note: Whenever we multiply or divide the denominator by any number, we also need to multiply or divide the same number by the numerator also. If the student is not multiplying the numerator also, then the answer so obtained would be wrong.