A proper fraction is a fraction with the numerator (top number) less than the denominator (bottom number), e.g. $1/3 \;;\; 3/4 \;;\; 5/7 \;;\; 6/7$. It is always less than 1.
An improper fraction is a fraction with the numerator larger than (or equal to) the denominator, e.g. $7/6 \;;\; 8/4 \;;\; 3/3 \;;\; 8/7 \;;\; 34/9$. It is always greater than or equal to 1.
A mixed number is a whole number and a proper fraction combined. Thus, it is always greater than 1.
Each improper fraction can also be expressed as a mixed number.
How to convert an improper fraction to a mixed number.
To convert $15/7$ into a mixed number, we need to find out how many times 7 can fit into 15. For this divide the numerator by the denominator:
$15÷7=2$ with remainder 1 ($15=2×7+1$).
2 will be used as the whole number of mixed number and 1 will be the numerator above the denominator.
How to convert a mixed number into a fraction:
Multiply the whole number by the denominator:
A mixed number can be also written as: 15⁄8 ; 33⁄4.