Fractions are an important part of math. They help us show parts of a whole.

There are three main types of fractions:

1. Proper fractions
2. Improper fractions
3. Mixed numbers

Let’s focus on proper and improper fractions.

Proper Fractions:

A proper fraction is one where the top number (called the numerator) is smaller than the bottom number (known as the denominator). This means the value of the fraction is less than one.

For example:

• $\frac{3}{4}$ (3 is less than 4)
• $\frac{2}{5}$ (2 is less than 5)

You can think of proper fractions like slices of a pie. If you have a pie cut into 4 pieces and you eat 3 slices, you have $\frac{3}{4}$ of the pie left.

Improper Fractions:

Improper fractions are different. In these fractions, the top number is bigger than or equal to the bottom number. This means the fraction is equal to or greater than one.

For example:

• $\frac{5}{4}$ (5 is greater than 4)
• $\frac{6}{6}$ (6 is equal to 6)

Using the pie analogy again, if you take 5 slices from a pie that only has 4 slices, you have more than one whole pie. This is shown by the fraction $\frac{5}{4}$.

Mixed Numbers:

Sometimes, it helps to turn an improper fraction into a mixed number. A mixed number combines a whole number with a proper fraction.

For example, $\frac{7}{4}$ can be written as $1 \frac{3}{4}$. This means you have 1 whole pie and $\frac{3}{4}$ of another pie.

Understanding proper and improper fractions is important. They are the building blocks for more advanced math that you will learn in 8th grade and beyond!