Types of Fractions

A fraction is essentially a part of the whole where the numerator is the part
and the denominator is the total whole.
For example - $1 \over 8$ pizza will describe one pizza slice out of $8$ pizza slices that exist in a family-sized pizza.
Another example:
If there are $3$ balls in a bag and only $2$ of them are pink, we can say that the pink balls constitute $2 \over 3$ of the balls in the bag.

A simple fraction is the classic among all fractions and contains only a numerator and a denominator.

The fraction line - symbolizes the division operation. 
The numerator – represents the part of the whole (the relevant part we are asked about in the question – the thing that needs to be divided equally among everyone). 
The denominator – represents the whole – the total – the total number of "pieces" there are. 

For example:
Dana had a birthday cake. Dana's mom cut the cake into $20$ equal slices.
At the birthday party, the children ate $15$ slices of cake in total, including Dana.
Present a simple fraction that represents the part of the cake that remains.
Solution:
The part of the cake that was eaten is $15$ slices out of $20$, which means there are $5$ slices left out of $20$, which is: $5 \over 20$.
If we simplify, we get $1 \over 4$.

Click here to learn more about a simple fraction

An improper fraction is any number written like a fraction with a numerator and a denominator, but it is actually a whole number or a whole number with a fraction.
How can you remember this? 
The word "improper" indicates that the fraction we see is not really a simple fraction but an improper one – "similar" to a simple fraction but actually it is not because it is whole or more than whole and not just a part of a whole.

Exercise:
In the orange cake recipe, you need one and a half cups of flour.
Describe the amount of flour in the cake using an improper fraction.

Solution:
A cup and a half is actually $1 \frac{1}{2}$. Now let's convert this mixed number to an improper fraction:

We multiply the number of wholes by the denominator.
To the result we obtained, we add the numerator – the final result will be the new numerator.
In the denominator – we don't change anything.

We get:
$3 \over 2$

Click here to learn more about improper fractions

A mixed number is a fraction composed of a whole number and a fraction, hence its name – it combines both whole numbers and fractions.
The whole number appears to the left of the fraction, followed immediately by the fraction.
Examples of mixed numbers:

$4 \frac{3}{5}$

$11 \frac{9}{10}$

$2 \frac{1}{2}$

Advanced Exercise:
Romi asked her mom how much longer until their vacation in Spain.
Her mom replied: exactly two weeks and three days.
Represent the time until the vacation as a mixed number.

Solution:
Note, we need to express two weeks and three days using a mixed number.
Therefore, we express the two weeks as $2$ as a whole number and the three days as $3 \over 7$, meaning three days out of a week.
(The whole number in this case represents $2$ full weeks)
We get that: $2\frac {3}{7}$ is the duration in a mixed number until the vacation in Spain.

Click here to learn more about mixed fractions

A decimal fraction represents a non-whole number using a decimal point.
The decimal fraction can be without whole numbers at all or with whole numbers.
The decimal point divides the fraction as follows:

Another example:

We will check the whole numbers – the decimal fraction with the larger whole number is the greater one.
If the whole numbers are the same, we will check the digits after the decimal point.
We will go digit by digit in order (starting from the tenths, hundredths, and so on).
If they are identical, we will continue.
If they are different, we will determine which fraction is greater accordingly.

Click here to learn more about decimal fractions