Solving Percent Problems: IS/OF

Joseph THompson

13 Mar 201309:55

EducationalLearning

32 Likes 10 Comments

TLDRThis instructional video script teaches viewers how to solve percentage problems using a simple 'is over of' trick. It guides the audience through setting up proportions and solving a series of examples, including finding what percentage of a number equals a given value and vice versa. The script also covers word problems involving percentages, such as determining the number of students with A's in a class and calculating the original price of an item after a discount. The method simplifies the process, making it accessible for students to tackle various percentage-based questions.

Takeaways

📝 The importance of having a math notebook for note-taking during the video lesson is emphasized.
🔢 A simple trick for solving percent problems is introduced: setting up a proportion with the percent over 100.
📚 The first example problem is to find what number 25% of it equals 6, using the proportion method.
🧐 The process of solving the example involves multiplying the given percentage by 100 and dividing by the result to find the unknown number.
🤔 The script encourages students to check their answers using number sense, like verifying if 6 is indeed 25% of 24.
📈 The second example asks to find what percent of 40 equals 28, and the solution involves setting up a proportion and solving for the variable.
📝 The script explains how to test the answer by comparing equivalent fractions or proportions.
📉 Another problem involves finding what number 15% of 60 is, with a step-by-step guide on setting up and solving the proportion.
🤓 The script helps students understand the reasonableness of their answers by comparing them to known percentages.
📚 The transcript explains how to solve word problems involving percentages, such as determining how many students have A's based on a given percentage.
💰 An example of a word problem about finding the original price of a book given a discounted price is provided, with a step-by-step solution.

Q & A

What is the key trick mentioned in the script for solving percent problems?
-The key trick mentioned in the script for solving percent problems is to set up a proportion using the formula 'is over of', where the percentage is placed over 100 and the other ratio is set up accordingly.
How do you set up a proportion to find what number 25% represents if it equals 6?
-To find what number 25% represents when it equals 6, you set up the proportion as 25/100 = 6/x. Solving for x gives you x = (6 * 100) / 25, which simplifies to x = 24.
What is the process to determine what percent of 40 is 28?
-To determine what percent of 40 is 28, you set up the proportion as (28/40) = x/100. Solving for x gives you x = (28 * 100) / 40, which simplifies to x = 70, meaning 28 is 70% of 40.
How can you verify your answer for the problem 'What percent of 40 is 28'?
-You can verify your answer by setting up the equivalent fractions 70/100 and 28/40, and simplifying both to see if they are the same. In this case, both simplify to 7/10, confirming the answer is correct.
What is the solution for the problem '15 percent of 60 is what number'?
-To find what number 15 percent of 60 is, you calculate (60 * 15) / 100, which simplifies to 9. So, 15 percent of 60 is 9.
How can you check if the answer to '15 percent of 60 is what number' is reasonable?
-You can check the reasonableness of the answer by comparing it to known percentages. For example, 0% of 60 is 0, and 50% of 60 is 30. Since 15% is less than 50%, the answer of 9 is reasonable.
What is the solution for the problem 'What percent of 20 is 18'?
-To find what percent of 20 is 18, you set up the proportion as (18/20) = x/100. Solving for x gives you x = (18 * 100) / 20, which simplifies to x = 90, meaning 18 is 90% of 20.
In the script, how many math students does Mr. Thompson have according to the problem?
-According to the script, Mr. Thompson has 33 math students.
How many of Mr. Thompson's math students have A's if 21.21% of them do?
-To find how many students have A's, calculate 33 * 21.21 and then divide by 100, which gives approximately 6.993. Since you can't have a fraction of a student, you round up to 7 students.
What was the original price of the book if Mr. Thompson paid 85% of the original price and it cost him $17?
-To find the original price, set up the proportion as 17 = x * 85%. Solving for x gives you x = 17 / (85/100), which simplifies to x = $20.
What is the significance of rounding up in the context of the problem about Mr. Thompson's math students?
-The significance of rounding up in the context of the problem is that you cannot have a fraction of a student, so the number of students with A's is rounded up to the nearest whole number, which is 7.

Outlines

00:00

📚 Solving Percent Problems with Proportions

This paragraph introduces a simple trick for solving percentage problems using proportions. The instructor emphasizes the importance of having a math notebook and provides a step-by-step guide on setting up a proportion for percentage problems. Examples are given, such as finding what number 25% is of when the result is 6, and what percent of 40 is 28. The solutions are explained in detail, including the method of checking answers using number sense and equivalent fractions. The paragraph concludes with a problem involving 15% of 60, guiding the learner through the process of finding the correct answer.

05:06

📘 Applying Percentages to Word Problems

The second paragraph extends the concept of percentages to word problems, which are more complex and require a deeper understanding of the 'is over of' relationship. The instructor provides a problem involving Mr. Thompson's math students and their grades, explaining how to set up a proportion to find out how many students received an 'A'. Another word problem involves calculating the original price of a book when a discount is applied. The paragraph encourages practice and understanding of these concepts, ensuring that learners can apply them to various real-life scenarios.

Mindmap

Keywords

💡Percent Problems

Percent problems refer to mathematical problems that involve percentages. In the video, these problems are addressed by setting up proportions to find unknown values. The script uses the phrase 'is over of' to simplify the process, as seen in examples like '25% of what number is 6'.

💡Proportion

A proportion is an equation that shows two ratios are equal. In the context of the video, proportions are used to solve percent problems by setting up an equation where the percentage is over 100, and the other ratio is the given numbers in the problem, such as '25% over 100 equals 6 over x'.

💡Variable

In mathematics, a variable represents an unknown value that we are trying to find. In the script, the variable is used in the context of setting up equations to solve for the unknown number in percent problems, like 'of what number is my variable'.

💡Number Sense

Number sense is the intuitive understanding of numbers and their relationships. In the video, it is used to check the correctness of the solution to a percent problem, such as asking 'is six twenty-five percent of 24' to verify the answer.

💡Equivalent Fractions

Equivalent fractions are fractions that represent the same value but have different numerators and denominators. The script mentions testing the correctness of a solution by simplifying equivalent fractions, like '70 over 100 equals 28 over 40'.

💡Word Problems

Word problems are mathematical problems that are presented in a narrative or real-world context. The video script includes word problems to demonstrate the application of the 'is over of' method in more complex scenarios, such as 'Mr. Thompson has 33 math students, 21.21% of how many have A's'.

💡Original Price

Original price refers to the price of an item before any discounts or changes. In the script, there is a word problem that involves finding the original price of a book given a discounted price, 'Mr. Thompson bought a book for 85% of the original price if he paid $17'.

💡Discount

A discount is a reduction in the original price of an item. The video script uses the concept of a discount to illustrate a word problem, where the original price is determined from a given discounted price, as in '85% of the original price'.

💡Math Notebook

A math notebook is a tool used for recording mathematical work and problems. The script emphasizes the importance of having a math notebook for note-taking during the explanation of percent problems.

💡Practice Problems

Practice problems are exercises designed to help learners apply and reinforce their understanding of a concept. The video script mentions practice problems to give the audience an opportunity to apply the 'is over of' method to new scenarios.

Highlights

The importance of having a math notebook for note-taking during the video.

A simple trick for solving percent problems using the 'is over of' method.

Instructions to pause the video to write down problems for practice.

Setting up a proportion to solve percent problems, with examples provided.

Explanation of how to solve '25% of what number is 6' using the proportion method.

Verification of the solution using number sense for the problem of finding 25% of a number.

Demonstration of solving 'what percent of 40 is 28' using the proportion method.

Another method of verifying the solution by simplifying equivalent fractions.

Instructions to write down and attempt the problem '15 percent of 60 is what number'.

Explanation of the reasonableness of the answer for 15% of 60 being 9.

Introduction to solving word problems using the 'is over of' relationship.

Problem-solving example: 'What percent of 20 is 18' with step-by-step guidance.

Understanding the key concept of setting up a proportion for percentage with a total.

Solving a word problem involving Mr. Thompson's math students and their grades.

Rounding up the answer to the nearest whole number in the context of students.

Solving a word problem about Mr. Thompson buying a book at a discounted price.

The final note on practicing problems and the expectation of reviewing answers.

Transcripts

Browse More Related Video

Math 7 4 7 Homework Help Morgan

Math Antics - Finding A Percent Of A Number

Easy Percentage Trick you were Never Taught at School!

Algebra SYSTEM WORD PROBLEM – Let’s solve it step-by-step...

Using Density and Molarity to Solve for the Percent by Mass of a Solution

Solving Percent Problems: IS/OF

Takeaways

Q & A

What is the key trick mentioned in the script for solving percent problems?

How do you set up a proportion to find what number 25% represents if it equals 6?

What is the process to determine what percent of 40 is 28?

How can you verify your answer for the problem 'What percent of 40 is 28'?

What is the solution for the problem '15 percent of 60 is what number'?

How can you check if the answer to '15 percent of 60 is what number' is reasonable?

What is the solution for the problem 'What percent of 20 is 18'?

In the script, how many math students does Mr. Thompson have according to the problem?

How many of Mr. Thompson's math students have A's if 21.21% of them do?

What was the original price of the book if Mr. Thompson paid 85% of the original price and it cost him $17?

What is the significance of rounding up in the context of the problem about Mr. Thompson's math students?