What is an Improper Fraction? (Definition and Examples)

• Definition: An improper fraction is a heavy-top fraction where the Numerator (top number) is greater than or equal to the Denominator (bottom number).
• Meaning: Mathematically, this simply means that the total value of the fraction is greater than 1 whole.

• $\frac{7}{4}$ (Seven-fourths): The top number (7) is bigger than the bottom number (4). It is improper.
• $\frac{15}{2}$ (Fifteen-halves): The top (15) is bigger than the bottom (2). It is improper.
• $\frac{5}{5}$ (Five-fifths): The top is exactly equal to the bottom. This is also officially classified as an improper fraction, representing exactly 1 whole.

Imagine a pizza is cut into exactly 4 slices (Denominator = 4).

• If you eat 3 slices, you ate $\frac{3}{4}$ of a pizza. This is a normal, 'Proper' fraction.
• But what if you are extremely hungry and eat 7 slices? You ate $\frac{7}{4}$. How is that physically possible? It is possible because you ate one entire full pizza (4 slices), opened a second pizza box, and ate 3 slices from that one! You ate more than 1 whole pizza.

Because improper fractions look heavy and awkward, we usually convert them into Mixed Fractions (a whole number + a small fraction).

• Take $\frac{7}{4}$.
• Simply divide 7 by 4.
• $4$ goes into $7$ exactly 1 time (This is the whole number). The remainder is 3.
• So, $\frac{7}{4}$ is converted into the mixed fraction: $1 \frac{3}{4}$ (One and three-fourths).