How To Simplify Division Fractions – Welcome to this free step-by-step guide to dividing fractions. This guide will teach you how to easily divide fractions by fractions (and fractions by whole numbers) using a simple three-step method called Hold-Change-Flip.
Here are some examples of how to use the Keep-Change-Flip method to divide fractions and explain why it works for any math problem that involves dividing fractions. Plus, this free guide includes animated video lessons and free practice worksheets with answers!
How To Simplify Division Fractions
Before learning how to divide fractions using the Keep-Change-Flip method, you need to make sure you understand how to multiply fractions together (it’s easier than dividing!).
Simplifying Ratios No Units
Since multiplying fractions is usually taught before dividing fractions, you probably already know how to multiply two fractions together. If so, you can skip to the next section.
Rule for Multiplying Fractions: When multiplying fractions, multiply the numerator first and then the denominator as follows…
Now that you know how to multiply fractions, you’re ready to learn how to divide fractions using the simple 3-step Keep-Change-Flip method.
Simplifying Fractions Is Just Not That Simple!
To solve this example (and any problem where fractions must be divided, we’ll use the Keep-Change-Flip method)
If we consider 1/2 ÷ 1/4 in the form of the problem: how much is 1/4 in 1/2?
Then, if we visualize 1/4 and 1/2, we can clearly see that 1/2 is 2 1/4, so the final answer is 2.
How To Divide Fractions
As in example 01, you can use the save change method to solve this problem:
What if you had to divide fractions by whole numbers? It turns out that this process is exactly the same as the previous example!
Note that in this example you are dividing fractions by whole numbers. But converting whole numbers to fractions is actually quite easy. All you have to do is rewrite the number as a fraction with the number itself in the numerator and 1 in the denominator.
Simplifying Algebraic Fractions
Now that you have rewritten the whole numbers as fractions, you can use the Keep-Change-Flip method to solve this problem.
Check out the video lessons below to learn more about dividing fractions by fractions and dividing fractions by whole numbers:
Looking for some extra sharing practice? Click the link below to download your free worksheet and answers: We use cookies to make things great. By using our website, you agree to our cookie policy. cookie settings
Multiplication And Division Of Fractions Interactive Worksheet
This article was co-authored by staff. Our team of trained editors and researchers check articles for accuracy and comprehensiveness. Our content management team closely monitors our editorial work to ensure that each article is backed by solid research and meets our high quality standards.
A fraction with a fraction in both numerator and denominator is called a complex fraction. These types of expressions can be intimidating, especially if they are algebraic expressions that involve variables. If you remember that commas are the same as commas, it becomes easier to simplify them. To simplify a complex number, first transform it into a division problem. Then divide as you would any fraction by a fraction. Remember to take the inverse of the second part and multiply. When working with variables, it is important to remember certain algebraic rules for simplifying expressions.
This article was co-authored by staff. Our team of trained editors and researchers check articles for accuracy and comprehensiveness. Our content management team closely monitors our editorial work to ensure that each article is backed by solid research and meets our high quality standards. This article has been viewed 25,713 times. Ok, I’m ready to share my amazing method of dividing one part with another. Well, maybe not surprising…like Andrew Wills’ proof of Fermat’s last theorem…but at least interesting. Best of all, fun and student friendly!
Dividing Fractions By Whole Numbers
Last week I asked if anyone had any tips on how to make dividing fractions easier for students. I said I would share the trick after hearing from you.
I got a great response from Michelle, who said that she used the mnemonic “KFC” (like fried chicken) in her classroom for Keep-Change-Flip. The idea is that you keep the first quotient, then change the sign from multiplication to division. Finally, you turn the second part, on the right side. The site where we live has a similar mnemonic with the phrase: Copy-Dot-Flip, “dot” meaning multiplication dot.
But what I want to share with you is a completely different method of dividing one part into another, which saves time and is easier and, in my opinion, more fun than the standard method.
Fractions For Kids Explained: How To Teach Your Child Fractions At Home
The method I’m going to show you works for any complex partial situation you might encounter, such as:
In this blog post, I’ll limit my chat to complex arithmetic-type parts, meaning those with only numbers and no variables. I will do another post later on using this same process for the algebraic parts if that seems important.
So what exactly is this magical method? Well, it’s based on something I learned the other day when I just didn’t mess around dividing fractions by fractions. I realized that after you do a KFC or Copy-Dot-Flip, what you get – in general – is actually quite easy to understand, as the following image will show you, and a quick proof:
Multiplying & Dividing Fractions (1.1.3)
If you think about it, the terms in the numerator of the result – the terms a and d – have something in common; they are outside the original complex number, so I call the terms “outside”. Also, the terms b and c in the denominator of the result are inside the complex number, so I call them “inside”.
So when dividing fractions in this vertical format, the answer is simply multiply the outside by the other divided by the inside by multiplying each other.
I find it easy for students to remember and easy to do. The following table summarizes this idea and provides an interesting way to remember this concept by imagining the set of terms as the fraction “sandwich”.
Dividing Fractions: Using The Shortcut
So, in other words, the plural quarter you start with can be thought of as a sandwich with two slices of bread on top and bottom and a slice of bologna and cheese in the middle.
The bottom line is that to simplify fractional sandwiches, all you have to do is put two slices of bread together for the numerator and multiply, then put together the bologna and cheese denominator and multiply.
With this idea, simplifying these complex parts becomes much easier. Here’s a picture of how it’s done and how this method saves time compared to the method we’ve been taught to use backwards.
How To Divide Fractions: From Annoying To Fun!
There is even more good news. This new way of looking at complex fractions also gives students a great new way to simplify fractions before they get the answer. When you simplify completely, the answer will be the part that is completely reduced, so you don’t need to emphasize that part.
So now you might want to see the whole process from start to finish so you can decide for yourself if this method is right for you. Well, that’s exactly what we’re going to show you next. As you can see I used pink to highlight the outside and yellow to highlight the inside.
Finally, you might say, a “harder” problem. But check it out. Is it really harder than what we just did? You decide.
Simplifying An Expression With A Fraction Bar
In my next blog, I’ll ask you some of these questions so you can get used to this technique and begin to cut down on those precious seconds and nanoseconds you spend doing homework so you can spend more time doing all the things you want to do. more: texting, watching YouTube, hiking, skating (roller and ice), etc. You know better than me.
Josh Rappaport is the author of five math books, including the Parents’ Choice Award-winning Algebra Survival Guide. If you like the way Josh explains these questions, you’ll love The Algebra Survival Guide and companion workbook, both available on Amazon.com. Just click the link in the sidebar for more information!
Division, elementary math, fractions, making math fun, math tricks, using analogies when teaching math, using color when teaching math, using stories We use cookies to create beauty. By using our website, you agree to our cookie policy. cookie settings
Divide The Following Fractions Show Your Complete Solution And Simplify Your Answer If Possible.pa
This article was co-authored by Dr. Mario Banuelos. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With more than eight years