Multiply the following fractions:
A. \[\dfrac{2}{5} \times 5\dfrac{1}{4}\]
B. \[6\dfrac{2}{5} \times \dfrac{7}{9}\]
C. \[3\dfrac{2}{5} \times \dfrac{4}{7}\]
D. \[2\dfrac{3}{5} \times 3\]

Hint: First convert all the mixed fraction numbers into a proper or improper fraction numbers and then multiply the numerators and the denominators of both the numbers together separately to find their multiples.

Complete step-by-step answer:
Given the numbers
A. \[\dfrac{2}{5} \times 5\dfrac{1}{4}\]
Here the second number is in mixed fraction so first convert it into a improper fraction by multiplying the whole number part by the fraction’s denominator and then add it by fractions numerator as
 \[5\dfrac{1}{4} = \dfrac{{\left( {5 \times 4} \right) + 1}}{4} = \dfrac{{21}}{4}\]
Now since we have both the numbers to be multiplied in the same form so we will multiply them as
  \[\dfrac{2}{5} \times \dfrac{{21}}{4} = \dfrac{{21 \times 2}}{{20}}\]
By solving this we get
 \[ \Rightarrow \dfrac{{42}}{{20}} = \dfrac{{21}}{{10}} = 2.1\]
Hence the multiple of the fraction \[\dfrac{2}{5} \times 5\dfrac{1}{4} = 2.1\]
So, the correct answer is “2.1”.

B. \[6\dfrac{2}{5} \times \dfrac{7}{9}\]
Here the first number is in mixed fraction so first convert it into an improper fraction as
 \[6\dfrac{2}{5} = \dfrac{{\left( {6 \times 5} \right) + 2}}{5} = \dfrac{{32}}{5}\]
Now since we have both the numbers to be multiplied in the same form so we will multiply them as
  \[\dfrac{{32}}{5} \times \dfrac{7}{9} = \dfrac{{32 \times 7}}{{45}}\]
By solving this we get
 \[\dfrac{{224}}{{45}} = 4.9\]
Hence the multiple of the fraction \[6\dfrac{2}{5} \times \dfrac{7}{9} = 4.9\]
So, the correct answer is “4.9”.

C. \[3\dfrac{2}{5} \times \dfrac{4}{7}\]
Here the first number is in mixed fraction so first convert it into an improper fraction as
 \[3\dfrac{2}{5} = \dfrac{{\left( {3 \times 5} \right) + 2}}{5} = \dfrac{{17}}{5}\]
Now since we have both the numbers to be multiplied in the same form so we will multiply them as
  \[\dfrac{{17}}{5} \times \dfrac{4}{7} = \dfrac{{17 \times 4}}{{35}}\]
By solving this we get
 \[\dfrac{{68}}{{35}} = 1.94\]
Hence the multiple of the fraction
 \[3\dfrac{2}{5} \times \dfrac{4}{7} = 1.94\]
So, the correct answer is “1.94”.

D. \[2\dfrac{3}{5} \times 3\]
Here the first number is in mixed fraction so first convert it into an improper fraction as
 \[2\dfrac{3}{5} = \dfrac{{\left( {5 \times 2} \right) + 3}}{5} = \dfrac{{13}}{5}\]
Now since we have both the numbers to be multiplied in the same form so we will multiply them as
  \[\dfrac{{13}}{5} \times 3 = \dfrac{{39}}{5}\]
By solving this we get
 \[\dfrac{{39}}{5} = 7.8\]
Hence the multiple of the fraction
 \[2\dfrac{3}{5} \times 3 = 7.8\]
So, the correct answer is “7.8”.

Note: A fraction of a numbers where the numerator is larger than its denominator is known as the improper fraction, in the number \[\dfrac{9}{5}\] here \[9\] is the numerator and \[5\] is the denominator and \[9 > 5\] . Now in a fraction of a number when the numerator is smaller than its denominator then the number is known as the proper fraction and its value will always be less than 1.