Algebra 2 8-5 Complete Lesson: Adding and Subtracting Rational Expressions

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! At 3 P.M., four runners all leave the starting line, running laps around the indoor track.

If the runners maintain their pace, at what time with Sue, Drew, and Stu finish a lap together?

Problem 2 Got It? Consider the expression below and use it to match responses from the left to the items on the right.

x ≠ -1
x ≠ 0
x ≠ 1
x ≠ 2

What is the sum of the two rational expressions in simplest form?
Identify any restriction(s) on the variable.

Problem 2 Got It? Consider the expression below and use it to match responses from the left to the items on the right.

x ≠ -2
x ≠ -1
x ≠ 1
x ≠ 2

What is the sum of the two rational expressions in simplest form?
Identify any restriction(s) on the variable.

Problem 2 Got It? Reasoning: Is it possible to add the rational expressions in Problem 2 by finding a common denominator, but not the least common denominator? Explain.

Problem 5 Got It? Suppose Option 3 is to buy a new hybrid that will get double the milease of the present hybrid. The SUV mileage stays the same. Which of the three options will give the best combined mpg?

Error Analysis: Describe and correct the error made in simplifying the complex fraction.

Open-Ended: Write an addition expression containing two rational expressions that that simplifies to this expression.

Review Lesson 8-4: Consider the expression below. Use it to match the correct response(s) from the left with each item on the right.

x ≠ -3
x ≠ -2
x ≠ 0
x ≠ 2
x ≠ 3

What is the quotient in simplest form?
Identify any restriction(s) on the variable.

Review Lesson 7-4: Write the logarithmic expression as a single logarithm.

Review Lesson 6-6: Let f and g be defined as follows.
Evaluate each expression on the right and match the appropriate value from the left.

82
57
30
101
3.75

Review Lesson 1-4: Solve the equation. Check your answer.
Enter only a number in fraction form.

Vocabulary Review: Identify the least common multiple [LCM] of each pair on the right. Match the appropriate LCM from the left with each pair.

3
12
20
24
14x2
14x

4 and 5
6 and 12
2x and 7x

Use Your Vocabulary: Categorize each statement on the left as true or false.

The fraction below is a complex fraction.
The fraction below is a complex fraction.

True
False

100

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Solve It! At 3 P.M., four runners all leave the starting line, running laps around the indoor track.

If the runners maintain their pace, at what time with Sue, Drew, and Stu finish a lap together?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It? Consider the expression below and use it to match responses from the left to the items on the right.

Problem 2 Got It? Consider the expression below and use it to match responses from the left to the items on the right.

Problem 2 Got It? Reasoning: Is it possible to add the rational expressions in Problem 2 by finding a common denominator, but not the least common denominator? Explain.

Problem 3 Got It?

Problem 3 Got It?

Problem 4 Got It?

Problem 4 Got It?

Problem 5 Got It? Suppose Option 3 is to buy a new hybrid that will get double the milease of the present hybrid. The SUV mileage stays the same. Which of the three options will give the best combined mpg?

Error Analysis: Describe and correct the error made in simplifying the complex fraction.

Open-Ended: Write an addition expression containing two rational expressions that that simplifies to this expression.

Review Lesson 8-4: Consider the expression below. Use it to match the correct response(s) from the left with each item on the right.

Review Lesson 7-4: Write the logarithmic expression as a single logarithm.

Review Lesson 6-6: Let f and g be defined as follows.
Evaluate each expression on the right and match the appropriate value from the left.

Review Lesson 1-4: Solve the equation. Check your answer.
Enter only a number in fraction form.

Vocabulary Review: Identify the least common multiple [LCM] of each pair on the right. Match the appropriate LCM from the left with each pair.

Use Your Vocabulary: Categorize each statement on the left as true or false.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Algebra 2 8-5 Complete Lesson: Adding and Subtracting Rational Expressions

Solve It! At 3 P.M., four runners all leave the starting line, running laps around the indoor track.If the runners maintain their pace, at what time with Sue, Drew, and Stu finish a lap together?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It? Consider the expression below and use it to match responses from the left to the items on the right.

Problem 2 Got It? Consider the expression below and use it to match responses from the left to the items on the right.

Problem 2 Got It? Reasoning: Is it possible to add the rational expressions in Problem 2 by finding a common denominator, but not the least common denominator? Explain.

Problem 3 Got It?

Problem 3 Got It?

Problem 4 Got It?

Problem 4 Got It?

Problem 5 Got It? Suppose Option 3 is to buy a new hybrid that will get double the milease of the present hybrid. The SUV mileage stays the same. Which of the three options will give the best combined mpg?

Error Analysis: Describe and correct the error made in simplifying the complex fraction.

Open-Ended: Write an addition expression containing two rational expressions that that simplifies to this expression.

Review Lesson 8-4: Consider the expression below. Use it to match the correct response(s) from the left with each item on the right.

Review Lesson 7-4: Write the logarithmic expression as a single logarithm.

Review Lesson 6-6: Let f and g be defined as follows. Evaluate each expression on the right and match the appropriate value from the left.

Review Lesson 1-4: Solve the equation. Check your answer. Enter only a number in fraction form.

Vocabulary Review: Identify the least common multiple [LCM] of each pair on the right. Match the appropriate LCM from the left with each pair.

Use Your Vocabulary: Categorize each statement on the left as true or false.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Solve It! At 3 P.M., four runners all leave the starting line, running laps around the indoor track.

If the runners maintain their pace, at what time with Sue, Drew, and Stu finish a lap together?

Review Lesson 6-6: Let f and g be defined as follows.
Evaluate each expression on the right and match the appropriate value from the left.

Review Lesson 1-4: Solve the equation. Check your answer.
Enter only a number in fraction form.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.