A fraction is usually seen as a “part of a whole” (like 1/4). An improper fraction occurs when the top number (numerator) is larger than or equal to the bottom number (denominator).
As the diagram from Expresswala Academy shows:
“An improper fraction is a combination of a whole and a proper fraction.”
When you have enough parts to make a full circle or a full bar, you can represent that value as a mixed number (a whole number + a fraction).
Let’s look at a visual example. Imagine we are working with blocks divided into 4 equal parts. Each small piece is 1/4.
The First Whole: If we shade all 4 parts of one block, we have $4/4$, which equals 1 whole.
The Extra Part: If we have one more shaded piece from a second block, that is another 1/4.
The Math:
So, 5/4 is the improper fraction, and its mixed number version is $1 \frac{1}{4}$.
What if we have even more pieces? Let’s stay with our blocks of 4.
The First Whole: Again, 4 shaded pieces give us 1 whole ($4/4$).
The Extra Parts: This time, we have 3 extra shaded pieces from the next block. That is 3/4.
The Math:
Here, 7/4 is our improper fraction, which is the same as saying $1 \frac{3}{4}$.
To turn a whole number into a fraction so you can add it, just look at the denominator of the other fraction.
If you are working with fourths, 1 whole = 4/4.
If you are working with thirds, 1 whole = 3/3.
By adding the “whole” fraction to the “leftover” fraction, you get your improper fraction!