Add and Subtract Fractions with Unequal Denominators

I don’t know about you but when it comes to students learning about fractions with unequal denominators…it might as well be something similar to being thrust into the frozen tundra and told to survive for three days with no supplies.

For some students you can see the wheels turning but nothing being produced. Shear panic and confusion takes over.

As this takes place you can imagine teachers running and screaming through the halls. “They just don’t get it and I don’t know what else to do!!!”

When it comes to teaching fractions you have to start at base level. It’s like base camp before you climb Mt. Everest. You know the mountain your about to climb. You know you are going to climb it. You just want to come out on the other end unscathed.

We are embarking on teaching scholars the nuances of fractions.

It takes a lot of prep time along with ingenuity and some luck sprinkled in for good measure. I am sure their have been moments in the classroom where I was hoping a fairy would fly in and sprinkle some dust over everyone and then suddenly everyone has light-bulb moment we all strive for in our students.

When I am with a student after weeks and weeks of small group, one on one, and tutoring, it is at that moment, they begin staring at you like your an alien from another planet. We see words begin to form…and you know what they are going to say before they say it…”I don’t get it.”

I always have the image of that cartoon cat with those big sad eyes.

It is at that moment everyone sits down in a corner and begins to cry.

Of course this only happens during your annual observation and your left describing to your boss. “I swear…it was the fractions I tell you!”

What I have done is scrap all my teachings. Not literally scrap them but you know revamp them. I had to rethink where do I need to start and where do I want them to end up.

Because when you see a test question like this.

adding and subtracting unequal denominators
A test question written by me.

We know our students are not anywhere close to being able to answer these questions when we start. We need a plan to get them from where they are to where they need to be.

I usually follow plan like this

  • Understanding fractions
  • Estimating and adding fractions
  • Grasping Multiples
  • Adding and subtracting unlike denominators
  • Adding and subtracting unlike denominators in real world situations
  • Check for understanding

It takes me three or four days on the basics before I even get to the state curriculum we are suppose to teach.

Understanding Fractions

I will hand students this fraction strip set I created.

Fraction strips used for adding and subtracting unlike denominators
Fraction Strips

I will go over them real quick just so students know what they are looking at.

Then I will have them use this worksheet I created to tell me which fraction is larger?

Worksheet for determine which fraction is larger
Worksheet for fractions

I just want my students to start looking at fractions and seeing them. I want them to start making mental notes on how one fraction my look larger, because of the misconceptions they have, but realize its actually smaller.

I then switch from the fraction strips and begin using number lines.

Estimating and adding fractions

I use the number line and benchmark rule (0, 1/2, 1) mainly for estimating fractions. I have several worksheets I created and walk them through this process.

Grasping Multiples

This is where the rubber hits the road. In fifth grade they should know multiples from fourth grade. But not always. So again climbing Mt. Everest right. We need to make sure our climbers have the skill set in place.

I have a full teaching on discovering the LCM. Step by step. I even have them create there own multiplication chart they can use to help them. It pays dividends and I find we use it all year long in various situations. Especially in small group and one on one.

A great website to get multiplication charts is

Adding and subtracting unlike denominators

This is where we apply everything we learned and begin to actually add and subtract unlike denominators. I created a 4 day homework sheet, all on one page. Because we know in the school system paper is like gold. It can actually be bartered in the school. Best currency there is, especially at the end of the year.

But here I am demonstrating and then turning them lose walking around and clearing up misconceptions. Adding and subtracting unlike denominators in real world situations

Adding and subtracting unlike denominators in real world situations

It is at this stage that I am adding the rigor to what we have learned. This is where I want them to start seeing what they will experience in state tests. Using all kinds of shapes and scenarios to illustrate fractions.

This is where we are moving beyond so to speak. I want them to be challenged…causing them to think. It is here where I am moving them to the questions you saw above.

This is where I know what to reteach, how to set up small groups, what kind of math stations I need to create. It is that moment when you can see the summit of the mountain and know you are going to make it.

Check for understanding

Then you give the mother load. That test that they will see on your state test. It is here where you see if they can apply all the information you spent the last two weeks teaching.

Below I included some other goodies for you. You will see the vocabulary I teach. I even test them on those terms and have them create their own flash cards for these words.

Then you will see the misconceptions your students have when it comes to fractions.

Academic Vocabulary

  • Benchmark fractions: Fractions that are easy to round to and add and subtract with
  • Common denominators: When two fractions have the same denominator
  • Denominator: Tells the total number of equal parts or groups into which the whole or group has been divided
  • Equivalent fractions: Fractions that name the same part of a whole region, set, or distance on a number line
  • Fractions greater than one: A fraction whose numerator is greater than its denominator, sometimes referred to as an “improper fraction”
  • Mixed number: A whole number and fraction
  • Numerator: Counts how many equal parts are described
  • Simplest Form: The form of a fraction when the numerator and denominator have the number 1 as the greatest common factor.
  • Unequal denominators: Fractions with denominators that have different values, such as 6/9 and 8/12.

Here are some misconceptions students face when dealing with fractions.

misconceptions about fractions


Add and Subtract Unlike Denominator

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