Question

What is \[4\dfrac{2}{5}\] as an improper fraction?

Answer 1

Hint: This type of question depends on the conversion of mixed fraction into improper fraction. Mixed fraction is an addition of the whole number and its fractional part, here it is \[4+\dfrac{2}{5}\] . We need to multiply the whole number by the suitable form of 1, in this case it is \[\dfrac{5}{5}\] and then add the result to the fractional part of the mixed fraction.

Complete step by step answer:
Now, we have to find improper fraction of \[4\dfrac{2}{5}\]
We can write this mixed fraction as an addition of its whole part and fractional part.
\[\Rightarrow 4\dfrac{2}{5}=4+\dfrac{2}{5}\]
Now, we have to express 4 in terms of fraction which can be represented as \[4=4\times \dfrac{5}{5}=\dfrac{20}{5}\]
\[\Rightarrow 4\dfrac{2}{5}=\dfrac{20}{5}+\dfrac{2}{5}\]
By combining the numerators over common denominator we get,
\[\Rightarrow 4\dfrac{2}{5}=\dfrac{20+2}{5}\]
By simplifying the numerator we can write,
\[\Rightarrow 4\dfrac{2}{5}=\dfrac{22}{5}\]
Hence, the improper fraction of \[4\dfrac{2}{5}\] is \[\dfrac{22}{5}\].

Note: In this type of question students may convert the given mixed fraction into improper fraction as follows:
We know that a mixed fraction is a whole number plus a fractional part. An improper fraction is a fraction where the numerator is greater than the denominator. To convert mixed fraction into improper fraction multiply the whole number by the denominator and then add a numerator to it. Then write answers over the denominator.
Consider, \[4\dfrac{2}{5}\]
First we multiply whole number that is 4 by denominator that is 5
\[\Rightarrow 4\times 5=20\]
Then by adding numerator to it we get,
\[\Rightarrow 20+2=22\]
Finally, by writing the answer over the denominator we get,
\[\Rightarrow \dfrac{22}{5}\]
\[\Rightarrow 4\dfrac{2}{5}=\dfrac{22}{5}\]
Hence, the improper fraction of \[4\dfrac{2}{5}\] is \[\dfrac{22}{5}\].