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College Algebra: Help and Review27 chapters | 230 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When it comes to fractions in algebra, we hardly ever use mixed numbers. Instead, we opt for the ease of use of improper fractions. Watch this video lesson to learn how to change your mixed numbers to improper fractions.

In algebra, instead of using a **mixed number**, a fraction written with a whole number part and a fraction part that is less than 1, we use **improper fractions**, fractions whose numerator is greater than the denominator. In this video lesson, we will learn how to change your mixed numbers into improper fractions.

We use improper fractions over mixed numbers because they are easier to deal with in formulas and such. Recall that your mixed numbers look like 2 1/2, while your improper fractions look like 3/2. Changing your mixed number into an improper fraction isn't all that hard as it turns out. All you need to do is to be able to do a little multiplication and some addition.

So, let's look at the procedure for changing mixed numbers into improper fractions. It helps to think of your mixed numbers as pies. The whole number part tells you how many whole pies you have. The fraction part tells you how many more slices of a pie you get in addition to your whole pies. The denominator tells you how many slices each pie is cut into. When you think of it like this, the problem gets easier.

Your job now is to find the total number of slices you have. To do this, you are going to multiply your denominator, the number of slices each pie has, by the number of whole pies you have. This gives you the number of slices that you have in your whole slices. Now you are going to add the numerator of your fraction. This gives you how many more slices of pie you get.

After you have added, you now have the total number of pie slices. You are going to write this number on top of your denominator. Now you know how many pie slices you have and how many slices each pie is cut into. Let's look at how this works in a couple examples.

Let's convert 2 1/2 into an improper fraction. At first look, we see that we have two whole pies and a part of a third pie. The denominator tells me that my pies are into 2 slices each. So, I multiply this denominator by my whole number to find out how many slices I have from my whole pies. So, 2 * 2 = 4. I have 4 slices here. Now I need to add the number of slices from my partial third pie. 4 + 1 = 5. Ah, I have 5 slices in total. I write this number on top of my denominator, 5/2, and I am done.

Now, you try converting 5 1/4 into an improper fraction. Yes, multiply the 5 and the 4 first. You get 20. Good. Now add the 1. 21. Good. Now write it over your denominator. 21/4, and you are done!

Now, let's review. We've learned that in algebra we tend to use **improper fractions**, fractions whose numerator is greater than the denominator, over **mixed numbers**, a fraction written with a whole number part and a fraction part that is less than 1. A necessary skill then is to be able to turn those mixed numbers into improper fractions. To do this, we multiply the whole number part by the denominator and then add the numerator. We then put this total over our denominator, and we are done.

As you complete this lesson, you could:

- Recognize and write improper fractions and mixed numbers
- Work through example problems
- Convert mixed numbers to improper fractions

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College Algebra: Help and Review27 chapters | 230 lessons | 1 flashcard set

- What is a Fraction? - Definition and Types 6:20
- How to Raise and Reduce Fractions 6:17
- Relating Fractions and Decimals 6:32
- 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 Change Mixed Numbers to Improper Fractions 3:31
- 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
- Using the Number Line to Compare Decimals, Fractions, and Whole Numbers 6:46
- How to Solve Complex Fractions 5:20
- Addition, Subtraction, Multiplication, and Division with Decimal Notation 4:50
- Practice with Fraction and Mixed Number Arithmetic 7:50
- Estimation Problems using Fractions 7:37
- Solving Problems using Fractions and Mixed Numbers 7:08
- Go to Fractions

- Go to Factoring

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