 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.

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## 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:

[Image_Link]/cimages/multimages/16/frac_not_1.

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## Visualizing Fractional Notation

It’s said that a picture is worth a thousand words, so let’s look at some images that will help us understand fractional notation. The following image shows a bar broken into 5 equal pieces. Therefore, 5 pieces make up a whole bar in this example, so the denominator is 5. Of the 5 pieces, 2 are shaded in. Because we are referring to 2 of the 5 pieces, the numerator in this example is 2.

This image represents the fraction 2/5. ## 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.

[Image_Link]/cimages/multimages/16/frac_not_5.

png” alt=”5″ />

## Conversion

Sometimes it is easier to use improper fractions in an equation than a mixed number, so we need to know how to turn a mixed number into an improper fraction. To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number and the denominator.
2. Add the answer to step 1 to the numerator and this becomes the new numerator.
3. The denominator stays the same.

Let’s try going through the steps with 2 1/3.

Step 1: Multiply the whole number (2) by the denominator (3): 2 x 3 = 6Step 2: Add the answer (6) to the numerator (1): 6 + 1 = 7. The new numerator is 7.Step 3: The denominator (3) stays the same.The improper fraction for 2 1/3 is 7/3.

## You Try!

Let’s try one more and change 3 4/5 to an improper fraction.Step 1: Multiply the whole number (3) by the denominator (5): 3 x 5 = 15Step 2: Add the answer (15) to the numerator (4): 15 + 4 = 19. The new numerator is 19.Step 3: The denominator (5) stays the same.

The improper fraction for 3 4/5 is 19/5.

## Lesson Summary

We learned that fractional notation is made up of two parts, a numerator and a denominator. We also learned that we can convert a mixed number to an improper fraction.

In to remember which part goes where is
• In form for 3 1/2 is 7/2. Multiplying
• Improper numerator, and the denominator will stay
• Fractions the 2 with the slash between the
• In skinny legs? Well, you could say
• In 3/2 To demonstrate that these two fractions
• Improper from above to work out a
• Dividing can all be written as a
• Adding – 2 = 2 (2x – 1)(2(2x
• This and 20 can also be divided 