Taming the Terms: Simplifying Algebraic Expressions with Rational Numbers

Algebra 1 Grades High School 4:15 Video
Print Lesson Plan Watch Video

Lesson Description

Master the art of simplifying algebraic expressions containing fractions and decimals by combining like terms. This lesson will equip you with the tools to confidently tackle these types of problems.

Video Resource

Examples of simplifying expressions involving rational numbers |7th grade | Khan Academy

Khan Academy

Duration: 4:15
Watch on YouTube

Key Concepts

  • Combining Like Terms
  • Rational Numbers (Fractions and Decimals)
  • Distributive Property

Learning Objectives

  • Students will be able to identify like terms in algebraic expressions containing rational numbers.
  • Students will be able to simplify algebraic expressions by combining like terms with fractional and decimal coefficients.
  • Students will be able to apply the distributive property to simplify expressions before combining like terms.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concepts of 'like terms' and rational numbers (fractions and decimals). Briefly discuss the importance of order of operations.
  • Video Example 1: Decimals (10 mins)
    Watch the first example from the Khan Academy video, pausing at key points to explain the steps involved in combining like terms with decimal coefficients. Emphasize the importance of correct arithmetic with decimals.
  • Video Example 2: Fractions (10 mins)
    Watch the second example, focusing on combining like terms with fractional coefficients. Review how to add and subtract fractions with common denominators. Reinforce the commutative property to rearrange terms.
  • Video Example 3: Distributive Property (10 mins)
    Watch the final example, highlighting the use of the distributive property to eliminate parentheses before combining like terms. Emphasize the correct application of the distributive property with fractional coefficients.
  • Practice Problems (15 mins)
    Provide students with practice problems involving both decimals and fractions. Encourage students to show their work and check their answers. Circulate the classroom to provide support and answer questions.
  • Review and Wrap-up (5 mins)
    Review the key steps in simplifying expressions with rational coefficients. Answer any remaining questions and preview upcoming topics.

Interactive Exercises

  • Term Matching Game
    Create a matching game where students pair like terms with their coefficients. This reinforces the identification of like terms.
  • Simplify and Solve
    Present a series of expressions to simplify, and then provide a value for the variable(s). Students must first simplify the expression and then substitute the value to find the final answer.

Discussion Questions

  • What are 'like terms', and why is it important to identify them correctly?
  • How does the distributive property help simplify expressions?
  • What strategies can you use to avoid errors when working with fractions and decimals?
  • Can you give an example where combining like terms is helpful in a real-world scenario?

Skills Developed

  • Simplifying Algebraic Expressions
  • Working with Rational Numbers
  • Applying the Distributive Property
  • Problem-solving Skills

Multiple Choice Questions

Question 1:

Which of the following terms is a 'like term' with 3.5x?

Correct Answer: -1.2x

Question 2:

Simplify the expression: 2/3a + 1/3a - 5

Correct Answer: a - 5

Question 3:

Apply the distributive property: 2(x + 1/2)

Correct Answer: 2x + 1

Question 4:

Simplify: -2.5y + 6.2y

Correct Answer: 3.7y

Question 5:

Which property justifies changing 2/5x - 3/5x to -3/5x + 2/5x?

Correct Answer: Commutative Property

Question 6:

Simplify: 1/4m - 3/4 - 1/2m + 1

Correct Answer: -1/4m + 1/4

Question 7:

Which of the following is the simplified form of 0.75b - 0.25b + 1.5b?

Correct Answer: 2.0b

Question 8:

What is the first step in simplifying 3(1/3x - 2) + x?

Correct Answer: Apply the distributive property.

Question 9:

Simplify the expression: 5/8p - 1/4p

Correct Answer: 3/8p

Question 10:

What is the simplified form of -3(0.5x - 1) + 2x?

Correct Answer: 0.5x + 3

Fill in the Blank Questions

Question 1:

To simplify 2/7x + 5/7x, you should ____ the coefficients.

Correct Answer: add

Question 2:

The first step in simplifying 3(a + 2/3) is to apply the ____ property.

Correct Answer: distributive

Question 3:

____ terms have the same variable raised to the same power.

Correct Answer: like

Question 4:

Simplifying 4.8y - 1.2y results in ____.

Correct Answer: 3.6y

Question 5:

The simplified form of 1/5m + 4/5 - 3/5m is ____.

Correct Answer: -2/5m + 4/5

Question 6:

In the expression 5x + 3 - 2x, the like terms are ____ and ____.

Correct Answer: 5x and -2x

Question 7:

Simplifying 0.25a + 0.75a + a equals ____.

Correct Answer: 2a

Question 8:

To combine 5/6 and -1/3, you must first find a ____ ____.

Correct Answer: common denominator

Question 9:

After distributing, 2(0.5x - 4) becomes ____.

Correct Answer: x - 8

Question 10:

The opposite of 5/9x is ____.

Correct Answer: -5/9x

Educational Standards

A1.A.3.2:Simplify polynomial expressions by adding, subtracting, or multiplying. A1.A.3.4:Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans