Question

How do you simplify \[1\dfrac{1}{2}-2\dfrac{4}{5}\]?

Answer 1

Hint: In this problem, we have to simplify the given fraction. We can first convert the given mixed fraction into its improper fraction. We will then get two fractions, which should be subtracted. We will have different denominators, so we cannot subtract it directly. We can cross multiply the fraction to get a simplified form of the given fraction.

Complete step-by-step solution:
We know that the given fraction to be simplified is,
\[1\dfrac{1}{2}-2\dfrac{4}{5}\]
We can now convert the given mixed fractions to its improper fraction.
We can first take the numerator, multiply the whole number part 1 and the denominator 2 and add to the numerator 1. Write the result 3 in the numerator,
Similarly, we can take the denominator, multiply the whole number part 2 and the denominator 5 and add to the numerator 4. Write the result 14 in the numerator, we get
We can write it as,
\[\Rightarrow \dfrac{3}{2}-\dfrac{14}{5}\]
Now we can simplify the above step.
We can see that we have different denominators, so we cannot subtract it directly. We take the LCM of denominators of both fractions 2 and 5 and then divide the LCM with the denominators, then the divisor will be multiplied with the numerator now at the end we get a simplified form.
\[\Rightarrow \dfrac{5\times 3-14\times 2}{5\times 2}=\dfrac{15-28}{10}\]
We can now simplify the above step,
\[\Rightarrow -\dfrac{13}{10}\]
Therefore, the simplified form of \[1\dfrac{1}{2}-2\dfrac{4}{5}\] is \[-\dfrac{13}{10}\].

Note: Students make mistakes while converting the mixed fractions into its improper fraction, by multiplying the whole number part to the denominator and adding it to the numerator and finally write the result in the numerator. We should concentrate while cross multiplying the numbers.