Understanding Rational Expressions and Fractions

Mr. Holcomb presents a lesson on equivalent rational expressions, starting with an exercise on writing fractions equivalent to one-third. The lesson progresses to solving rational expressions, identifying undefined values, and reducing expressions to their lowest terms. Students are encouraged to work through exercises independently, with a focus on understanding restrictions to prevent division by zero. The lesson concludes with a summary of key concepts.

What is the main topic of Lesson 22?

• Understanding geometric shapes

• Graphing linear equations

• Equivalent rational expressions

• Solving quadratic equations

What is the purpose of the opening exercise in the lesson?

• To solve complex equations

• To write equivalent fractions to one-third

• To graph a polynomial function

• To calculate the area of a rectangle

What visual model is used to explain equivalent fractions?

• Tape diagram

• Pie chart

• Line graph

• Bar graph

How can you create a fraction equivalent to one-third using a tape diagram?

• Divide the rectangle into eight equal parts

• Divide the rectangle into two equal parts

• Divide the rectangle into four equal parts

• Divide the rectangle into six equal parts

What is a key consideration when working with rational expressions?

• Ensuring the denominator is not zero

• Ensuring the numerator is zero

• Ensuring both numerator and denominator are zero

• Ensuring the expression is undefined

In the example problem, what value of 'a' makes the expression undefined?

• a = 3

• a = 0

• a = 1

• a = 2

What should you do to solve for 'a' in the expression 6(a-1) - 3a = 0?

• Multiply both sides by 2

• Add 3a to both sides

• Subtract 6 from both sides

• Combine like terms and solve for 'a'

What is the first step in reducing a rational expression to its lowest terms?

• Multiply the numerator by the denominator

• Add the numerator and denominator

• Subtract the denominator from the numerator

• Factor the numerator and denominator

When simplifying rational expressions, what must be identified to prevent division by zero?

• Values of the numerator

• Values of the denominator

• Values of the constant term

• Values of the entire expression

What is the simplified form of the expression 2x + 2 + 2 over 2x squared + 5x + 2?

• x over 2x + 1

• 2x + 2 over x + 1

• 2x over x + 1

• 2 over 2x + 1