A mixed number is in the format a b/c. An improper fraction is in the format d/c. To convert a mixed number to improper fraction multiply the whole number by the denominator of the fraction and add the numerator.
Here a b/c = (ac + b)/c = d/c, where d = ac + b
An improper fraction is a fraction where the numerator is larger than the denominator. A mixed number is one that has both an integer and a fraction.
To convert a mixed number to an improper fraction you multiply the integer by the denominator and add the result of that to the numerator. For example
3 3/4 -- multiply the integer 3 by the denominator and get 12. Add the 12 to the numerator and you get 15. Keep the denominator the same.
Now, you have the improper fraction
I give you an example.
What is written to the left side of equal sign, 1 1/3, is the mixed number. The result, 4/3, is the improper fraction.
You notice that the integer 1 from the left side is written as the fraction 3/3 and the fraction 1/3 is added to the integer 1.
1 1/3 = 3/3 + 1/3 = 4/3
The improper fraction is formed from the numbers: 4 (dividend or numerator), 3 (divisor or denominator)
We'll write the reminder theorem:
4 = 3*1 + 1