Weight Loss Made a Bit Easier: Realistic and Practical Advice for Healthy Eating and Exercise
Available on Amazon.com in paperback/Kindle formats for $6.25/$2.99. Please click here for details.
Home | My Math and Education Books | Math Lessons | Ask a Math Question
Site Info | Contact Info | Tutoring Info | LarryZafran.com | Tweet
Lesson 37: More About Fractions
Fractions come up again and again in math. In this lesson you'll learn a bit more about how they work. Begin by reviewing Lesson 20.
Don't forget to watch the embedded video clip for this lesson at the bottom of the page. Please be sure to read the embedded video information and disclaimer.
We'll start with some definitions which need to be memorized. In a fraction, the top number is called the numerator, and the bottom number is called the denominator. These terms come up again and again.
In this lesson, just like in Lesson 20, I'll represent fractions using the slash format. For example, one-half will be written as 1/2.
Very often, we are asked to compare fractions. First make sure that you fully understand that a fraction is a number which describes part of a whole. When we talk about 1/2 of something, it doesn't matter what the size of shape of that thing is. We're just talking about one-half, in general. What this means is that if you are asked whether 1/2 is bigger than 1/3, there is no need to be concerned with what objects are actually being compared. We're just comparing the fraction of a whole that each fraction represents.
Let's look at what the numerator and the denominator of a fraction really mean. The denominator (bottom number) tells us how many equal parts the whole has been cut into. For example, a pizza is typically cut into 8 equal slices, so when we talk about pizza, we can talk about eighths. 8 would be the denominator. The numerator (top number) tells us how many parts of the whole we are dealing with. For example, if you eat 3 pizza slices, you have eaten 3/8 (three-eighths) of the whole pie.
A basic fact about fractions is that as the denominator (bottom number) gets bigger, the fraction gets smaller. Think about why this is the case. Imagine you cut a pizza into only 4 slices. Each slice would be quite big. If you ate one of those slices, you would have eaten 1/4 (one-fourth, or one-quarter) of the pie. If the pizza was cut into 8 slices, and you ate one of those, you would have only eaten 1/8 of the pie. You can see that 1/4 is a bigger number than 1/8. As the denominator gets smaller, the fraction gets bigger.
Certainly if fractions have the same denominator, then the fraction with the larger numerator is bigger. For example, 5/8 is bigger than 3/8 (e.g., 5 slices is more than 3 slices).
Another thing to understand about fractions is that if you multiply both the numerator and denominator by the same number, it does not change the fraction. For example, we can take the fraction 1/3, and multiply numerator and denominator by 2, to get 2/6. 2/6 is equivalent to 1/3. Sometimes we need to do this in order to more easily compare fractions. We can also divide both the numerator and denominator by the same number, if that will help us.
For example, which is bigger, 3/4 or 5/8? These fractions are hard to compare because they have different denominators. One deals with 4 pieces, and one deals with 8. Let's multiply both the numerator and denominator of the first fraction by 2, to get 6/8. I chose to multiply by 2, because I wanted to make sure that I ended up with a denominator of 8, and I know that 4 times 2 is 8. Now we can easily see that 6/8 is bigger than 5/8. You'll have more practice with this later.
Remember that you can
ask a math question if you have additional
questions about a topic, or you can
contact me if you have any comments
or suggestions for this site.