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ELM: CSU Math Study Guide16 chapters | 140 lessons

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Lesson Transcript

Instructor:
*Chad Sorrells*

Chad has taught Math for the last 9 years in Middle School. He has a M.S. in Instructional Technology and Elementary Education.

Improper fractions and mixed numbers are two different types of fractions. They both have different purposes when using fractions in a problem. In this lesson, you will learn how to convert between these two different forms.

An **improper fraction** is a fraction where the numerator is larger than the denominator. An example of this would be the fraction 12/8.

Improper fractions represent a value that is greater than the total value of one set. Often times, it's easier to leave your fraction in the improper fraction form to work with fractions. When multiplying and dividing fractions, you must use an improper fraction rather than mixed numbers.

**Mixed numbers** are fractions that contain a numerator, a denominator, and a whole number. These types of fractions contain whole sets and a fraction of the remaining set. An example of a mixed number would be 4 3/4.

Mixed numbers are used to represent the final answer when working with fractions. They are also helpful when adding and subtracting fractions.

The challenge with these two different forms of fractions is being able to convert between them easily. When converting an improper fraction to a mixed number, we will think of the fraction bar as division. For example, using the improper fraction 12/8, we would divide the numerator 12 by the denominator 8.

To convert an improper fraction to a mixed number, we will start by dividing the numerator by the denominator. Once you are finished dividing, your quotient will become your whole number. Your remainder will also become your numerator, and you will keep the same denominator.

Looking at the example, 12 will divide into 8 one time, with 4 left as our remainder. This will make our mixed number 1 4/8.

Let's check with a friend of mine, Adam, who works at a local cookie factory. Adam spends his day stacking delicious cookies into boxes that can hold 10 cookies each.

As he works steadily, the machine suddenly speeds up. Adam realizes that he has run out of boxes. In a panic, he presses the emergency stop button. Adam must go get enough boxes to pack the overflow of cookies. He counts the cookies and sees that there are 78 cookies to fit in the boxes that only hold 10 cookies each. Adam knows that the fraction to represent this would be 78/10.

Adam needs to change this improper fraction to a mixed number so that he can see how many boxes he needs. Adam begins by dividing the numerator 78 by the denominator 10. 10 will divide into 78 7 times. After subtracting, the remainder will be 8.

Adam can now see that the quotient 7 will become his whole number, the remainder 8 will become the numerator, and the denominator will stay 10.

Adam's mixed number is 7 8/10. Adam can see that he will be able to fill 7 full boxes and 8 out of 10 cookies in the next box. As he packs the last cookie, he presses the start button, and the machine starts sending more cookies down the line.

Occasionally when working with fractions, you will need to use an improper fraction. To change a mixed number to an improper fraction, we will multiply the whole number times the denominator. Next, we'll add that value and the numerator. This value will become your new numerator, and you will keep the same denominator.

Let's visit the local soccer fields where James is setting up the youth soccer league. James puts 8 kids on each team and has 3 kids left over. He currently has 9 3/8 teams. James knows that this means he has 9 full teams and 3 kids out of 8 left over.

James wants to know what number of kids signed up for soccer if he has 9 3/8 teams. To begin, James multiplies the whole number 9 times the denominator 8, which equals 72.

Now, using that value, 72, he will add the numerator, 3, which equals 75.

James know that he will keep the same denominator. So, the fraction that would represent the number of players playing soccer this season is 75/8.

So, in review, an **improper fraction** is a fraction where the numerator is larger than the denominator. **Mixed numbers** are fractions that contain numerators, denominators, and whole numbers.

To convert an improper fraction to a mixed number, we will start by dividing the numerator by the denominator. Once you are finished dividing, your quotient will become your whole number, your remainder will become your numerator, and you will keep the same denominator.

To change a mixed number to an improper fraction, multiply the whole number times the denominator. Next, you'll need to add that value and the numerator. This new value will become your numerator, and you will also keep the same denominator.

Following this lesson, you will be able to:

- Define improper fraction and mixed number
- Convert between improper fractions and mixed numbers
- Understand when it is appropriate to use each

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ELM: CSU Math Study Guide16 chapters | 140 lessons

- How to Build and Reduce Fractions 3:55
- How to Find Least Common Denominators 4:30
- Comparing and Ordering Fractions 7:33
- Changing Between Improper Fraction and Mixed Number Form 4:55
- How to Add and Subtract Unlike Fractions and Mixed Numbers 6:46
- Multiplying Fractions and Mixed Numbers 7:23
- Dividing Fractions and Mixed Numbers 7:12
- Practice with Fraction and Mixed Number Arithmetic 7:50
- Estimation Problems using Fractions 7:37
- Solving Problems using Fractions and Mixed Numbers 7:08
- How to Solve Complex Fractions 5:20
- Calculations with Ratios and Proportions 5:35
- Using Proportions to Solve Ratio Problems
- Practice Problems for Calculating Ratios and Proportions 5:59
- Go to ELM Test - Numbers and Data: Rational Numbers

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