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Adding and Subtracting Rational Expressions Worksheets

We are working with rational expressions here so they will be presented as fractions. Complete with a numerator and denominator. In this section we have them learn how to process sums and differences between a pair of them. This often starts by helping them recognize like terms. It also is a good idea to remind them that constants can be rewritten as factors for example: 28 = 7 x 4. This will help them in the simplification process. The ultimate goal here is to reshape the denominators, so that they are the same. If we can make that true, all we need to do is worry about the numerator. A great collection of worksheets to help students learn how to work sum and differences between two rational expressions.

Aligned Standard: HSA-APR.D.7

  • Adding Complex Expressions Step-by-step Lesson- The denominators always have kids a bit panicked to start with, but they learn quickly to use common factors.
  • Guided Lesson - We work on simplifying and combining. Express your answer as a single fraction in simplest form.
  • Guided Lesson Explanation - The best strategy here is to focus on getting common denominators and then taking it from there.
  • Practice Worksheet - We work on several variations of this skill and try to get them to settle down quickly.
  • Matching Worksheet - Match the problem to its simplified form. Take note of the variables that are present.
  • Common Factors Five Pack - I threw this one in here to help students review the factor and simplifying skills needed to be make these problems easier.
  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

Sheet 1 is addition, followed by both addition-subtraction, and we end of with just subtraction.

  • Homework 1 - In order to add the expressions, they must have a common denominator. The least common multiple (LCM) of 5 and 4 is 20.
  • Homework 2 - To subtract rational expressions with common denominators, subtract the numerators.
  • Homework 3 - To add rational expressions with common denominators, add the numerators. The first thing we must do is to find common denominators for the expressions.

Practice Worksheets

Version 1 and 3 are mixed operations. Version 2 is just subtraction.

  • Practice 1 - Express your answer as a single fraction in simplest form.
  • Practice 2 - The expressions have a common denominator, so you can subtract the numerator.
  • Practice 3 - We need to reduce the fraction that is present in all portions of the expression.

Math Skill Quizzes

Unlike the other sheets, the quizzes are all mixed sum and difference operations.

  • Quiz 1 - Factor the following expressions and see if you can ground them.
  • Quiz 2 - Find those commonalities. That is the key to making these easier to work with.
  • Quiz 3 - Sometimes its just one integer that solves the whole thing for you.

How to Add and Subtract Rational Expressions

Smile Square

Algebra becomes more complicated as we start to make further progressions that require us to combine or evaluate multiple expressions in the same system. However, complications do not mean they get difficult. It just means you have to learn a bit more. Similar is the case for adding and subtracting rational algebraic expressions. These are expressions that can often be written as a quotient of two polynomials.

When we need to calculate a sum or difference between two rationale expressions. The first thing we need to do is spot like terms and if we cannot spot them, we can often reduce the terms to create like terms. We then want to try to make the denominators the same. If we can make them the same then all we need to do is subtract or add the values of the numerator. We are often trying to find the Least Common Denominator (LCD). Let us consider an example and solve it manually.

Consider an example 1/3a + 1/4b. Let's sequentially solve this sum.

The denominators are not the same; therefore, we will have to find the LCD. The LCD is the product of the two denominators stated above. That means 3a × 4b = 12ab

So, to make the denominator 12ab, we have to multiply the first fraction by 4b/4b and the second fraction with 3a/3a.

1/3a × 4b/4b + 1/4b × 3a/3a

4b/12ab + 3a/12ab

Since the denominators are now the same, you have to the right the common denominator. You cannot add the numerators because both of them have separate variables.

(3a + 4b) / 12ab

Similarly, you can do the same for subtracting two rational expressions as well.

A Quick Trick to Incorporate with This Skill

The tag line was kind of catchy. I just wanted to point out something you should get in the habit with when evaluating any expression, but it does apply to this and can make your job much easier. The simple tip is just to reduce the expression to the lowest form before you begin to evaluate the operation whether it is addition or subtraction. A rational expression is simply two polynomials that are set in a ratio. Take your time and see if there are variables or constants available in both portions of the ratio and reduce them. In most cases, it will save you a great deal of time while working with the actual expression.

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