Question

How do you write $ 2\dfrac{2}{7} $ as an improper fraction?

Answer 1

Hint: We can see here that the given term is $ 2\dfrac{2}{7} $ a mixed fraction. It can be converted into an improper fraction i.e., where numerator is greater than the denominator and there is no whole number before the fraction by multiplying the denominator with the whole number and adding the numerator to obtain the new numerator of improper fraction, keeping the denominator same.

Complete step-by-step answer:
(i)
As we know that a fraction represented with its quotient and the remainder is a mixed fraction. In simpler words, it is a combination of a whole number and a proper fraction. Therefore, the fraction given to us i.e., $ 2\dfrac{2}{7} $ is a mixed fraction where $ 2 $ is the quotient and $ 2 $ is the remainder, $ 7 $ being the divisor.
And, we are asked to convert the given fraction to an improper fraction i.e., when the numerator is greater than the denominator.
Therefore, to convert a mixed fraction to an improper fraction, first we have to multiply the denominator of the mixed fraction with the whole number written before the fraction.
Here, as we can see the denominator is $ 7 $ and the whole number its $ 2 $ , multiplying the two will give us,
  $ 7 \times 2 = 14 $
(ii)
Now, we will add this product to the numerator of the mixed fraction i.e., $ 2 $ . So, after adding we will get:
  $ 14 + 2 = 16 $
(iii)
The product we added with the numerator value of the mixed fraction, now becomes the new numerator for the improper fraction. Therefore, the numerator of the improper fraction is $ 16 $ .
Whereas, in the case of the denominator, the value remains the same for an improper fraction as given by the mixed fraction. Therefore, the denominator of the improper fraction is $ 7 $ .
(iv)
The last step is to combine the numerator and the denominator together to get an improper fraction. Therefore, we get:
  $ \dfrac{{16}}{7} $
Hence, the improper fraction of $ 2\dfrac{2}{7} $ is $ \dfrac{{16}}{7} $ .
So, the correct answer is “ $ \dfrac{{16}}{7} $ ”.

Note: Remember, we do not have to change the value of the denominator when converting from a mixed fraction to an improper fraction. It remains the same in both. We could also solve this problem by writing the whole number as a fraction with the same denominator as the proper fraction present in the mixed fraction. For example, we could have written $ 2 $ as $ \dfrac{{14}}{7} $ and then add both the fractions to obtain its equivalent improper fraction.