Complete 8.3 Independent Practice Page 221 Answer Key: Step-by-Step Solutions & Teacher Copy

8.3 Independent Practice Page 221 Answer Key

Stuck on lesson 8.3 independent practice? You’ve come to the right place. This guide provides the complete answer key for page 221, along with detailed step-by-step solutions, video walkthroughs for tricky problems, and a printable PDF for teachers and students. We’ll break down common mistakes, review the core concepts, and offer extra practice to help you master the material.

Quick Answer: Full Answer Key for 8.3 (Page 221)

Below is the complete list of answers for the independent practice on page 221. For select problems, you can find a full explanation in the step-by-step solutions section. Always double-check your work against the final answer to identify where you might need more practice.

Note: Answers involving decimals may require rounding to a specific place value, such as the nearest hundredth. Be sure to follow the instructions provided in your textbook.

Step-by-Step Solutions (Selected Problems)

Getting the right answer is important, but understanding the process is even better. Here are detailed walkthroughs for some of the more challenging problems from page 221.

Problem #7: Calculating a Discount

Question: A shirt originally priced at $16 is on sale for 15% off. What is the sale price?

• Step 1: Convert the percent to a decimal.
  To work with the percentage, convert it into a decimal by dividing by 100.
  15% = 15 / 100 = 0.15
• Step 2: Calculate the discount amount.
  Multiply the original price by the decimal form of the discount.
  Discount = $16 × 0.15 = $2.40
• Step 3: Find the final sale price.
  Subtract the discount amount from the original price.
  Sale Price = $16.00 – $2.40 = $13.60
• Final Answer: The sale price is $13.60.

Problem #8: Finding the Whole from a Part

Question: At a school, 120 students are in the band. This represents 75% of the students in the eighth grade. How many students are in the eighth grade?

• Step 1: Set up the percent equation.
  The formula is Part = Percent × Whole. We know the Part (120 students) and the Percent (75%). We need to find the Whole.
  120 = 0.75 × Whole
• Step 2: Isolate the “Whole”.
  To find the total number of students, divide the part by the percent (in decimal form).
  Whole = 120 / 0.75
• Step 3: Solve the equation.
  120 ÷ 0.75 = 160
• Final Answer: There are 160 students in the eighth grade.

Video Walkthroughs & Quick Tips

Sometimes seeing a problem worked out visually makes all the difference. Here are short video guides for a couple of problems from lesson 8.3.

Video 1: Solving Word Problems with Percentages (Problem #13)

This video covers how to set up and solve word problems that involve finding the total when you only know a percentage.

(Video Embed Placeholder)

• Transcript & Timecodes:
  • 0:00 – Identifying the “part” and the “percent” in the word problem.
  • 0:45 – Setting up the equation to find the “whole”.
  • 1:30 – Solving the division and checking the answer.

Video 2: Calculating Percent Increase/Decrease (Problem #15)

Learn the formula for calculating percent change and apply it to a practical example.

(Video Embed Placeholder)

• Transcript & Timecodes:
  • 0:00 – Formula for percent change: (New - Old) / Old.
  • 0:55 – Plugging in the numbers from the problem.
  • 1:45 – Converting the final decimal into a percentage.

Printable PDF Answer Key & Teacher Copy

For offline study or classroom use, you can download a printer-friendly PDF version of this answer key. The file includes the final answers, notes on common mistakes, and key formulas from lesson 8.3. This resource is free for personal and educational use.

[Download the 8.3 Independent Practice Page 221 Answer Key PDF Here]

Common Student Mistakes on Page 221 (And How to Avoid Them)

It’s easy to make small errors when working with percentages. Here are some common mistakes students make on this assignment and how to prevent them.

1. Forgetting to Convert the Percent: Before multiplying or dividing, always convert the percentage to a decimal (e.g., 65% becomes 0.65) or a fraction (65/100).
2. Confusing “Part” and “Whole”: When a problem says “40 is 20% of what number?”, the “part” is 40 and the “whole” is unknown. The word “of” often points to the whole.
3. Calculating the Discount Instead of the Final Price: After finding the discount amount (e.g., 15% off $100 is $15), remember to subtract it from the original price to get the final sale price ($85).
4. Mixing Up Percent Increase and Decrease: Always use the formula (New Value - Original Value) / Original Value. A negative result indicates a decrease, while a positive result indicates an increase.
5. Rounding Errors: Pay close attention to instructions on rounding. If you need to round to the nearest cent, you must look at the third decimal place.

Problem Types Covered in 8.3 — Topic Breakdown

Lesson 8.3 focuses on applying percentages in various real-world scenarios. Understanding the different types of problems will help you recognize what formula to use.

• Finding the Part: These problems give you the whole and the percent, and you need to find the part.
  • Example: What is 25% of 80?
  • Solution: 0.25 × 80 = 20
• Finding the Whole: These problems give you the part and the percent, and you need to find the original total amount.
  • Example: 30 is 60% of what number?
  • Solution: 30 / 0.60 = 50
• Finding the Percent: These problems give you the part and the whole, and you need to figure out the percentage.
  • Example: 10 is what percent of 50?
  • Solution: (10 / 50) × 100 = 20%

Quick Practice Problems (Extra) + Answers

Feel like you need a little more practice? Try these problems, which are modeled after those on page 221. The answers are listed below.

1. What is 40% of 150?
2. A team won 12 games, which was 80% of the games they played. How many games did they play in total?
3. A recipe calls for 2 cups of sugar, but you only use 1.5 cups. What percentage of the sugar did you use?
4. A jacket costs $80 and is on sale for 25% off. What is the discount amount?
5. If 45 students in a survey represent 15% of the school’s population, how many students are at the school?

Answers:

1. 60
2. 15 games
3. 75%
4. $20
5. 300 students

How to Use This Answer Key Responsibly

An answer key is a powerful study tool when used correctly. Its purpose is to help you learn, not to bypass the work.

• For Students: Try to solve every problem on your own first. Use this key to check your answers. If you got an answer wrong, go through our step-by-step solutions to understand where you made a mistake. True learning happens when you identify and correct your errors.
• For Teachers and Parents: This guide can help you quickly check homework and identify which concepts your students are struggling with. Use the “Common Mistakes” section to guide your instruction and help your child or student avoid frequent pitfalls.

Where This Material Likely Comes From (Textbook & Edition)

The lesson “8.3 Independent Practice” on page 221 is a common structure in many middle school math curricula. This specific problem set is most frequently associated with the Go Math! series for Grade 6, 7, or 8, published by Houghton Mifflin Harcourt.

However, different states and school districts use customized versions or older editions. The page number might shift slightly between editions (e.g., 2014 vs. 2018 edition). Always confirm the chapter title, which is typically “Percents” or “Applying Percents,” to ensure you are working on the correct lesson.

Frequently Asked Questions (FAQ)

Where can I find the answer key for 8.3 independent practice page 221?

This page provides a complete answer key, step-by-step solutions, and a downloadable PDF for lesson 8.3 on page 221. The full answer table is available at the top of this article.

What textbook contains lesson 8.3 on page 221?

This lesson is most commonly found in the Go Math! middle school series. However, other math programs may use a similar numbering system.

How do you solve problem #7 on page 221?

Problem #7 requires you to calculate a discount and then subtract it from the original price. We provide a full, step-by-step explanation for this problem in the solutions section above.

Is there a printable answer key for 8.3 independent practice?

Yes, a link to a free, printable PDF version of the page 221 solutions is available in the “Printable PDF” section of this guide.

Pros & Cons of Using Online Answer Keys

Online resources can be incredibly helpful, but they come with their own set of advantages and disadvantages.

• Pros:
  • Immediate Feedback: Quickly check your work without waiting for a teacher.
  • Identify Weaknesses: See which problem types you consistently get wrong.
  • Accessibility: Find help anytime you are studying.
• Cons:
  • Risk of Cheating: Copying answers without understanding the process hurts your learning.
  • Potential for Errors: Unofficial keys can sometimes contain mistakes.
  • Over-Reliance: Becoming dependent on a key can reduce your problem-solving confidence.

Summary & Next Steps

Mastering percentages is a critical skill, and practice is the best way to get there. This guide provided the 8.3 independent practice page 221 answer key, along with tools to help you understand the material on a deeper level.

Your next steps should be:

1. Rework any problems you got wrong without looking at the solution.
2. Review the common mistakes to ensure you don’t make them on a test.
3. Try the extra practice problems to build your confidence.

If you found this guide helpful, download the printable PDF to keep as a study aid for your next quiz or test.

Also Read: