Question

How do you simplify \[2\dfrac{7}{10}-3\dfrac{7}{20}\]?

Answer 1

Hint: In the given question, we have been asked to simplify the fractions. In order to solve the question, first we need to convert the mixed fractions into improper fractions. After that we subtract the resultant fractions by making the denominator same by taking the LCM i.e. least common factor. Simplifying the fraction by subtracting the fraction and you will get the required solution.

Complete step by step solution:
We have given that,
\[\Rightarrow 2\dfrac{7}{10}-3\dfrac{7}{20}\]
Converting mixed fraction into improper fraction,
\[\Rightarrow 2\dfrac{7}{10}=\dfrac{10\times 2+7}{10}=\dfrac{27}{10}\]
And
\[\Rightarrow 3\dfrac{7}{20}=\dfrac{20\times 3+7}{20}=\dfrac{67}{20}\]
According to the question,
Combining both the improper fraction according to the question given, we get
\[\Rightarrow 2\dfrac{7}{10}-3\dfrac{7}{20}=\dfrac{27}{10}-\dfrac{67}{20}\]
Subtracting the numbers in the fraction by taking the LCM i.e. least common factor,
As we know that,
LCM of 10 and 20 is 20.
\[\Rightarrow \dfrac{27}{10}-\dfrac{67}{20}=\dfrac{27\times 2}{10\times 2}-\dfrac{67}{20}\]
Simplifying the above numbers in the fraction, we get
\[\Rightarrow \dfrac{54}{20}-\dfrac{67}{20}\]
Subtracting the above fractions, we get
\[\Rightarrow -\dfrac{13}{20}\]
Therefore,
\[\Rightarrow 2\dfrac{7}{10}-3\dfrac{7}{20}=-\dfrac{13}{20}\]
Hence, it is the required solution.

Note: A fraction is known as a part of the whole number. Fractions are of three types; one is proper fraction, second is improper fraction and the third is mixed fraction. A fraction is said to be a proper fraction if the numerator of the fraction is less than the denominator of the given fraction and the fraction is said to be improper fraction if the numerator is more than or equal to the denominator of that given fraction. A fraction is said to be mixed fraction if a whole number and the proper fraction are given side by side.