Question

How do you simplify \[\dfrac{2\dfrac{1}{3}}{1\dfrac{2}{5}}\]?

Answer 1

Hint: In this problem, we have to simplify the given fraction. We can first convert the given mixed fractions in the numerator and the denominator into its improper fraction, we can then use the rule for dividing fractions, which reciprocals the given division of fractions. We can then simplify the step to get the simplified form of the given fraction.

Complete step by step solution:
We know that the given fraction is,
\[\dfrac{2\dfrac{1}{3}}{1\dfrac{2}{5}}\]
We can now convert the mixed fraction into its improper fraction.
We can first take the numerator, multiply the whole number part 2 and the denominator 3 and add to the numerator 1. Write the result 7 in the numerator,
Similarly, we can take the denominator, multiply the whole number part 1 and the denominator 5 and add to the numerator 2. Write the result 7 in the numerator, we get
\[\Rightarrow \dfrac{\dfrac{7}{3}}{\dfrac{7}{5}}\]
We can now divide these fractions by using the rule of dividing fractions,
\[\Rightarrow \dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a\times d}{b\times c}\] …… (1)
Where a = 7, b = 3, c = 7, d = 5.
We can substitute these values in (1), we get
\[\Rightarrow \dfrac{7\times 5}{3\times 7}\]
We can now simplify the above step by cancelling the similar terms, we get
\[\Rightarrow \dfrac{5}{3}\]
Therefore, the simplified form of \[\dfrac{2\dfrac{1}{3}}{1\dfrac{2}{5}}\] is \[\dfrac{5}{3}\].

Note: Students make mistakes while converting the mixed fractions into its improper fraction, by multiplying the whole number part to the numerator and adding it to the denominator and finally write the result in the numerator. We should also concentrate while substituting values in the rule for dividing factors.