Question

Find the solution of $ 20\dfrac{1}{2} \times 19\dfrac{1}{2} $

Answer 1

Hint: The question has two mixed fractions. To find the value of the given arithmetic expression, we need to convert the mixed fraction into an improper fraction. After converting, we can multiply the two numbers. While multiplying, we multiply the numerators and the denominators to get a fraction. Then simplify that fraction to get the final answer.

Complete step-by-step answer:
Let us consider $ 20\dfrac{1}{2} $
This can be converted to improper fraction like this,
 $ 20\dfrac{1}{2} = \dfrac{{\left( {20 \times 2} \right) + 1}}{2} $
Which will give,
 $ 20\dfrac{1}{2} = \dfrac{{41}}{2} $
Now, the second one is $ 19\dfrac{1}{2} $
This can also be converted into improper fraction,
 $ 19\dfrac{1}{2} = \dfrac{{\left( {19 \times 2} \right) + 1}}{2} $
Which is,
 $ 19\dfrac{1}{2} = \dfrac{{39}}{2} $
Now, we multiply these two terms,
 $ \eqalign{
  & = \dfrac{{41}}{2} \times \dfrac{{39}}{2} \cr
  & = \dfrac{{1599}}{4} \cr} $
When we divide $ \dfrac{{1599}}{4} $ we get $ 399 $ as the denominator and a remainder of $ 3 $ .
Therefore, we write the whole number as is, write the remainder as the numerator and the denominator remains the same.
Hence, $ \dfrac{{1599}}{4} $ can be written as an improper fraction as $ 399\dfrac{3}{4} $
Therefore, the answer is $ 399\dfrac{3}{4} $ .
So, the correct answer is “ $ 399\dfrac{3}{4} $ ”.

Note: An improper fraction is a type of fraction where the numerator is greater than the denominator. A mixed fraction is a type of fraction which is formed by combining a whole number and a fraction. Improper fractions are used to make simplifications rather than mixed fractions because improper fractions are easier to solve.