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High School Algebra I: Homework Help Resource25 chapters | 271 lessons

Instructor:
*Jessica Williams*

Fractions aren't as confusing as most people think. Learn how fractions work by examining a few of their common uses in everyday life. Then, test your new knowledge with a post-lesson quiz.

Imagine that you and a group of friends are trying to decide what to do for fun this weekend. Three of your friends would enjoy ice skating, but you and two other friends would prefer fishing at the local lake. So you are at an impasse: three vote for skating, and three vote for fishing. In other words, half of your group wants one thing, while half wants the other. Whether you realize it or not, by dividing your group into halves, you are thinking with **fractions**.

Basically, a fraction describes how a part of a group relates to the whole group. To illustrate, think about a related word: fracture. If you drop a plate on the ground and it fractures into many pieces, you might be worried about picking up each piece to recreate the whole plate, making sure there are no leftover pieces on the ground. The plate fractured into many pieces, but you can still visualize it as a complete unit. Likewise, fractions represent complete groups that have been fractured, or broken apart, in some way. Fractions help us understand how those pieces fit into the original group.

So when you look at a fraction, you will see the number that represents the pieces (the fractured section) on the top of the division line. This number on the top is called the **numerator**. The number on the bottom represents how many total parts are in the group, and this number is called the **denominator**. To easily tell these two parts of the fraction apart, just remember that **d**enominator and **d**own both start with the letter **d**.

How would these abstract fractions look with real numbers? Take a look at the examples below.

Let's begin with an example from the kitchen: a carton of eggs. How many eggs could have possibly come in the carton in the picture below? We can count up all of the pre-made egg spaces in the carton to see that there is room for 12 eggs. That means that in this whole unit (the carton) there is the potential for 12 individual pieces. Since 12 represents the total number of possible members in the group, 12 must go in the denominator's position.

Now, look above at how many eggs are actually in the carton - 7 total. If we want to make a fraction that represents how many eggs are in the carton, we would put 7 in the numerator's position over the 12. However, what if we want a fraction to represent the empty spaces in the carton? Just add up the empty spaces (5 total) and put that sum in the numerator's position over the 12. We can see from this example that *fractions can represent sections of a group that are present OR sections that are missing*.

Also, can you tell which fraction is bigger? Well, we can see that there are more occupied egg spaces than empty spaces. That means that the fraction that represents the eggs in the carton is bigger. Thus, we can learn one other important truth about fractions: *when the denominators of two fractions are the same, the fraction with the larger numerator is the bigger fraction.*

Now think back to the group of friends at the beginning of this lesson. How can we use fractions to represent their different opinions about how to spend the weekend? Well, we must first determine the total number of people in our group, which is 6. This number will be the denominator. Then, we can create fractions based on the opinions of each section of the group. How many friends wanted to go fishing? Since there were 3 who wanted to fish, we can represent that part of the group with the fraction shown in the picture, 3/6.

But how did we know that our group was split in HALF before? Well, we knew that 3 is half of 6. This realization helps us discern another important truth about fractions. *Many fractions can be simplified*; in other words, they might look different, but they represent the same number. As you gain more experience working with fractions, it will be easier for you to identify equivalent fractions like these.

Refresh your memory of fractions during this lesson, then see how well you can:

- Recite the definitions of fraction, numerator, and denominator
- Remember real-life examples of fractions
- Realize the purpose of simplifying fractions

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High School Algebra I: Homework Help Resource25 chapters | 271 lessons

- What is a Decimal Place Value? 6:19
- Comparing and Ordering Decimals 8:56
- Addition, Subtraction, Multiplication, and Division with Decimal Notation 4:50
- Adding and Subtracting Decimals: Examples & Word Problems 6:53
- Multiplying and Dividing Decimals: Examples & Word Problems 5:29
- How to Estimate with Decimals to Solve Math Problems 8:51
- 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 Like Fractions and Mixed Numbers 4:14
- 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
- Using the Number Line to Compare Decimals, Fractions, and Whole Numbers 6:46
- How to Simplify Word Problems with Fractions Using Whole Numbers 3:38
- How to Reduce Fractions: Terms & Overview
- What are Fractions? - Definition & Examples
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