In this lesson, we will learn what fractional notation is and what it looks like.

We will also learn how to convert mixed numbers to fractional notation.

## Choices

If you had a choice between eating 1 1/3 of a candy bar or 4/3 of a candy bar, which would you choose? Did you know that a mixed number (like 1 1/3) and an improper fraction (like 4/3) can represent the exact same amount? These two numbers are equal, so no matter which one you chose, you would have the same amount of candy bar! This lesson will show you why this is true and how to convert mixed numbers to improper fractions.

## What Is Fractional Notation?

We use fractions when we are referring to a part of a whole instead of a whole number.

**Fractional notation** simply means that a number is written in fraction form. It is written as *a*/*b* where neither *a* nor *b* is equal to 0.A fraction has two parts, the numerator and denominator. The **numerator** is the number on top of the line and it represents how many pieces of the whole we are referring to. The **denominator** is the number below the line, and it represents how many pieces make up one whole. Look at these examples:

## Mixed Numbers in Fractional Notation

We can also write mixed numbers in fractional notation. A **mixed number** is one that consists of a whole number and a fraction. When we convert a mixed number to fractional notation, it makes an improper fraction.

An **improper fraction** is a fraction that represents more than one whole.The following image illustrates the mixed number 1 3/4. There are two circles that are each cut into 4 pieces. In this case, each whole is made up of 4 pieces, so the denominator is 4.

There are 7 pieces shaded, so the numerator is 7. The mixed number 1 3/4 is written as 7/4 in fractional notation.

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