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What are Fractions? - Definition & Examples

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.

Definition

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.

Examples

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 denominator and down both start with the letter d.

Parts of a fraction

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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.

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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.

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