Question

What is \[4\dfrac{2}{7}\] an improper fraction?

Answer 1

Hint: We are given a mixed fraction and we have to write it in the improper fraction form. Improper fraction refers to a fraction in which the numerator has a greater value than the denominator unlike the proper fraction, which has a numerator smaller than the denominator. So, in a mixed fraction we have a whole number and a fraction. Firstly, we will multiply the denominator and the whole number and add it to the numerator and the total value will be our numerator for the improper fraction. The denominator remains the same. Hence, we will have the improper fraction of the given mixed fraction.

Complete step-by-step solution:
According to the given question, we are given a mixed fraction and we have to write it in improper fraction.
An improper fraction refers to the fraction in which the numerator value is greater than the denominator unlike the proper fraction in which the numerator is smaller than the denominator.
The given mixed fraction we have is,
\[4\dfrac{2}{7}\]----(1)
We can see that the mixed fraction consists of a whole number and a fraction.
We will first multiply the denominator with the whole number and then add it to the numerator and the sum total of this expression is the numerator of the improper fraction. The denominator of the improper fraction is the same as the denominator of the mixed fraction. So, we have,
\[\Rightarrow \dfrac{\left( 7\times 4 \right)+2}{7}\]
Solving the above expression, we get,
\[\Rightarrow \dfrac{28+2}{7}\]
We will now add up the terms in the numerator, we get,
\[\Rightarrow \dfrac{30}{7}\]
Therefore, the improper fraction of the given mixed fraction is \[\dfrac{30}{7}\].

Note: While converting the mixed fraction into improper fraction, make sure that the multiplication of the denominator and the whole number is done correctly and then the adding with the numerator should also be done step wise and correctly. Also, the denominator of the improper fraction form of the mixed fraction remains unchanged and should be kept that way and should not be further multiplied or added to some other terms.