Multiplication and Fractions Explained
Understanding Fractions
Parts of a Whole
Fractions are a way of talking about pieces of something. Imagine you have a pizza that you're sharing with friends. If you cut it into eight equal slices and take one, you have a fraction of the pizza. Fractions help us describe amounts that aren't whole numbers.
Fractions are a way to represent parts of a whole.
Every fraction has two key parts: a numerator and a denominator. They are separated by a line.
Denominator
noun
The bottom number of a fraction that shows how many equal parts the whole is divided into.
The denominator tells you the total number of equal pieces that make up one whole thing. If you cut that pizza into eight slices, the denominator is 8.
Numerator
noun
The top number of a fraction that shows how many parts you have.
The numerator tells you how many of those pieces you're talking about. If you take three slices of that pizza, the numerator is 3. So, you have 3/8 of the pizza.
Types of Fractions
Fractions come in a few different flavors, depending on the relationship between the numerator and the denominator.
Proper Fractions: Smaller on Top A proper fraction has a numerator that is smaller than its denominator. This means it always represents a value less than one whole. For example, $1/2$ of a sandwich is less than a whole sandwich, and $3/4$ of a cup of flour is less than a full cup.
Improper Fractions: Bigger on Top An improper fraction has a numerator that is greater than or equal to its denominator. This means it represents a value that is one whole or more. If you have five quarters of a dollar, you have $5/4$, which is more than one whole dollar. If you have $4/4$ of a pizza, you have one whole pizza.
Mixed Numbers: A Mix of Whole and Part A mixed number combines a whole number and a proper fraction. It's another way to write an improper fraction. For example, instead of saying you have of a pizza, you could say you have and pizzas. This is written as .
| Type | Example | Meaning |
|---|---|---|
| Proper Fraction | The value is less than 1. | |
| Improper Fraction | The value is 1 or more. | |
| Mixed Number | A whole number and a fraction combined. |
Seeing is Believing
Visualizing fractions can make them easier to understand. Let's look at how we'd show an improper fraction and its equivalent mixed number.
Imagine we have the improper fraction . The denominator (4) tells us that each whole is made of four equal parts. The numerator (7) tells us we have seven of those parts.
To show this, we can draw two rectangles, each divided into four squares. We would shade in all four squares of the first rectangle (that's 4/4) and then three squares in the second rectangle (that's another 3/4). In total, we have seven shaded squares, or .
Looking at the same drawing, we can also see one completely full rectangle and another that is three-quarters full. This represents the mixed number . Both and represent the exact same amount.
Understanding these basic forms is the first step. Once you're comfortable telling them apart, you'll be ready for more.
Time to check your understanding.
In a fraction, what does the numerator represent?
In the fraction , what is the denominator?
Great work. You've now got the basics of what fractions are and how to describe them.