Fraction Division in Middle School Math
Have you ever taught fraction division to the students in your middle school math classes, only to find them "flipping" the wrong number?
Students may have been taught to "skip, flip, flip," "invert and multiply," or "multiply by the reciprocal." They may have "learned" the steps or learned a fun fraction division song to help them remember; but somehow they still flip the wrong one or they forget to flip at all. OR students change a mixed number into an improper fraction and seem to subconsciously think that since they did something to that mixed number, the flipping had already occurred...and then they don't flip anything. Why does this happen? I'm going to say that it happens because students don't understand why they're flipping anything  it doesn't mean anything to them. Fraction Division Using Common Denominators
So, I started using another way to teach fraction division  perhaps you've heard of it, or you already use it.
I never learned it this way as a student, but I like it, and it makes more sense to some students. I learned this method when I had a student teacher a few years back. She was teaching the fraction unit, and when her supervisor came in to observe and discuss, she asked if I had ever taught fraction division using common denominators. Having only learned (and then taught) to multiply by the reciprocal, of course I said no. The next time she visited, she brought me a page from a textbook that explained dividing fractions using common denominators. These are the steps:
I was shocked  it seemed SO simple! Fraction Division Example
Check out this example  it's a simple one, for starters:
5/6 divided by 2/3.
Fraction Division Example 2
Let's look at another one, with mixed numbers:
1_4/7 divided by 1_3/4.
Why Does Using Common Denominators Work?
Once the denominators are the same, we're dealing with fraction pieces that are the same size.
When we look at 5/6 ÷ 4/6, there are 5 pieces and 4 pieces that are the same size (our numerators). So, we're really looking at 5 ÷ 4, or how many times 4 fits into 5. Student Response to Dividing Fractions with Common Denominators
I teach both methods to my sixthgraders. Some really like it...it makes sense to them.
Others stick to the flipping method, but I don't know if this is because they like it better or because it was the first way they learned it.....most of them had been taught something about fraction division in 5th grade. Fraction Division Using the Reciprocal
Multiplying by the reciprocal  if students are going to use it, I think it's important that they understand WHY it works.
It may be tough for them to understand in 5th or 6th grade, but if they learn the common denominator method first, the proof may then make more sense to them. I found a great article on the NCTM website that uses the common denominator method to prove why multiplying by the reciprocal works  check it out, if you have time:) Fraction Division Math Wheels
Not too long ago, I made two math wheels, to use to teach both methods of dividing fractions  taking notes with the wheel will be more fun!
Students can save their wheel to use as a reference throughout the year. What do you think? Do you see any advantages or disadvantages to teaching fraction division using common denominators? Resources to teach and practice fraction division
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6 Comments
Marian Lemon
11/13/2017 05:58:10 pm
I have taught both methods to my 6th graders for several years. We talk about easy problems to use "same denominator" method versus using "keep, change, rearrange", or multiplying by the reciprocal.
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11/14/2017 02:14:17 am
This is brilliant. I have never seen this but I WILL be using it! I now teach 6th and 7th grade (always looking for ideas) but have taught 8th through PreCalculus also (18 years) and I have never seen it before but I LOVE IT!
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Annette McKee
11/14/2017 06:53:39 am
Definitely going to try this as my students have just struggled with a Fraction operations test.
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Mrs. S
5/25/2019 09:15:51 am
Neat trick. Will this help them when they get to Algebra and they're working with polynomials, or confuse them?
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1/27/2020 05:35:56 pm
These are some of the best ways to teach fractions. It presents visual objects and solid facts that cannot be forgotten in learner's mind.
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Barbara Madden
8/4/2021 08:38:43 am
If the division between the two numerators and the two denominators is clean with no remainders, you don't need a common denominator, let alone flip anything. For example, 1/6 divided by 1/3 equals 1/2. Notice the numerators divide to one, and the denominators divide to two giving you 1/2.
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AuthorHey there! I'm Ellie  here to share math fun, best practices, and engaging, challenging, easyprep activities ideas! Archives
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