LESSON: Mixed Numbers and Improper Fractions

INTRODUCTION

READ: Rewrite Mixed Numbers as Improper Fractions

Rewrite Mixed Numbers as Improper Fractions

A mixed number is a number that has both wholes and parts in it.

Example

Here we have a mixed number. We have five whole items and one-fourth of a whole.

Now you know how to identify a mixed number. The opposite of a mixed number is an improper fraction.

What is an improper fraction? An improper fraction is a fraction that has a larger numerator and a smaller denominator.

Example

If the denominator tells us how many parts the whole has been divided into, then this whole has been divided into 5 parts. The numerator tells us how many parts of the whole we have in this case, we have twelve parts.

If we have twelve out of five parts, then we have MORE than one whole. One whole would be five out of five parts, but we have 12 out of 5 parts. This is where mixed numbers come in.

How do we write a mixed number as an improper fraction? To write a mixed number as an improper fraction, we want to write a fraction in terms of parts instead of in terms of wholes and parts.

Example

Change to an improper fraction.

To do this, we multiply the whole number times the denominator and add the numerator.Then we put this over the original denominator.

2 3 + 1 7

Our original denominator is 3.

Our answer is .

Notice that the mixed number and the improper fraction are also equivalent.

EXAMPLE 1

READ: Rewrite Improper Fractions as Mixed Numbers

Rewrite Improper Fractions as Mixed Numbers

We just learned how to write a mixed number as an improper fraction. We can also work the other way around too, we can write improper fractions as mixed numbers.

How do you write an improper fraction as a mixed number?

First, remember that when you write an improper fraction as a mixed number, that you are converting a fraction in all parts to wholes and parts.

Example

If I have eighteen-fourths, I have eighteen parts and the whole has only been divided into 4 parts. This means that would be considered a whole.

When the numerator is larger than the denominator, you know that you have more than one whole. To change an improper fraction to a mixed number, divide the denominator into the numerator. This will tell you the number of wholes. If there are any left over, this tells you the fraction part.

18 4 4

But there are 2 left over because 4 4 = 16 and our numerator is 18. The left over part becomes the numerator over the original denominator.

Our answer is .

Our answer is .

Sometimes, you will have an improper fraction that converts to a whole number and not a mixed number.

Example

Here eighteen divided by 9 is 2. There isn’t a remainder, so there isn’t a fraction. This improper fraction converts to a whole number.

Our answer is 2.

EXAMPLE 2

READ: Compare and Order Mixed Numbers and Improper Fractions

Compare and Order Mixed Numbers and Improper Fractions

How do we compare a mixed number and an improper fraction?

We compare them by first making sure that they are in the same form. They both need to be mixed numbers otherwise it is difficult to determine which one is greater and which one is less than.

Example

The easiest thing to do here is to convert fifteen-fourths into a mixed number.

Now we know that six and one-half is greater than fifteen-fourths.

Our answer is .

How do we write mixed numbers and improper fractions in order from least to greatest or from greatest to least? We can work on this task in the same way as with the comparing. First, make sure that all of the terms you are working with are all mixed numbers.

Example

Write in order from least to greatest, .

We need to convert thirty-three halves and eighty-eight elevenths to mixed numbers.

Our answer is .

EXAMPLE 3

EXAMPLE 4

EXAMPLE 5

CHECK Yourself! Mixed and Improper Fractions