Simplify Expressions Containing Fractions by Combining Like Terms

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SWBAT simplify rational number expressions by combining like terms

Big Idea

We've simplified expressions with integers. Now it is time to focus on fractions - positive and negative.


2 minutes

The purpose of this section is to get students ready for rewriting fractions using common denominators.  Your students may not need this but I anticipate that mine will!  You may choose to use calculators with fraction operations and then skip this whole section.  That might be okay, but I tried to make sure the fractions had fairly friendly common denominators.

 I'll give students whiteboard and markers.

On the SmartBoard I'll write two numbers:  3 and 6.  I'll ask students to find the least common multiple.  Next I'll write 3 and 5, then 4 and 3, then 6 and 5.  You may notice that these are denominators from like terms in the guided problem solving section.  

Next I'll ask students to write fractions using a common denominator.  

I'll write the following pairs:  6 1/6 and 2/3, 1/3 and 1/4, 2/5 and 3/10.

This process can hopefully be done in only a few minutes.  



5 minutes

This lesson is presented as a short direct instruction lesson to create fluency on the objective.  I most closely associate this lesson with mathematical practice 8.  I have kept it short and simple so that students can focus on combining like terms with fractions and all that entails - common denominators, improper fractions, etc.

I will begin with the essential question:  How can you simplify rational number expressions?

There are 4 steps presented in the resource.  I placed in bold some of the properties or terms that we will use when justifying our steps in the example.

The work on the example will look like this:

1/2x + 1/2 + -5/8x + 1/6   additive inverse

1/2x + -5/8x + 1/2 + 1/6   commutative property

4/8x + -5/8x + 3/6 + 1/6  common denominators

-1/8x + 4/6 or -1/8x + 2/3


Guided Problem Solving

10 minutes

The guided problem solving section will be done with students working in pairs.  I have tried to start with simple problems and then increase the complexity.  The first problem does not require finding a common denominator.  The next problem requires a common denominator for only 1 pair of terms.  The next two examples require common denominators in both pairs of terms.  

For this work I will expect students to label their justifications as in the example problem.  This will help me when I am checking their work.  It will also help them to be through in their work.  

Independent Problem Solving

15 minutes

Students will work on these problems independently.  This problem set is built like the guided problem solving questions - they complexity increases.  I will expect student to simplify each problem in the step-by-step manner with justifications similar to the example.  

As students are working, I will mostly monitor the class and work.  Before answering any questions, I will expect students to have worked at least two steps.  It will be helpful to have these steps posted in the room or on the board, especially if you print this resource as a double sided copy.  That way students will not have to keep turning the paper over to see the next step.

Exit Ticket

5 minutes

Before we begin the exit ticket we will review the steps to simplifying expressions.  I may just cold card students to remind us of each step.  They can read from their notes if they'd like. 


There are only 3 questions on the exit ticket.  The like terms in problem 1 already have a common denominator so this should be the easiest.  Problem 2 only has 3 terms.  All of the problems in the packets had 4 terms so this should be easier.  Problem 3 requires students to find common denominators for each pair of like terms.

A successful exit ticket will be 3 out of 3.  If a student is able to do 2 out of 3, however, I know they are not far off from having this skill mastered.