Sergei Estimated $149 \%$ Of 67 By Performing The Following Steps. Which Statement Is True?$\[ \begin{array}{l} (70)(150 \%) \\ =(70)(100 \%+50 \%) \\ =(70)(100 \%)+(70)(50 \%) \\ =(70)(1)+(70)\left(\frac{1}{2}\right) \\ =70+35

In mathematics, percentages are often used to express a value as a fraction of 100. When dealing with percentages, it's essential to understand how to multiply and add them correctly. In this article, we will explore the concept of percentages and how to perform operations with them.

What is a Percentage?

A percentage is a way to express a value as a fraction of 100. It's denoted by the symbol "%" and is calculated by dividing the value by 100 and multiplying by 100. For example, 25% is equal to 25/100, which can be simplified to 1/4.

Multiplying Percentages

When multiplying percentages, we need to follow the order of operations (PEMDAS). This means that we need to multiply the numbers first and then add the percentages. In the given problem, Sergei estimated $149 \%$ of 67 by performing the following steps:

1. $(70)(150 \%)$
2. $=(70)(100 \%+50 \%)$
3. $=(70)(100 \%)+(70)(50 \%)$
4. $=(70)(1)+(70)\left(\frac{1}{2}\right)$
5. $=70+35$

Let's break down each step and understand what's happening.

Step 1: $(70)(150 \%)$

In this step, Sergei is multiplying 70 by 150%. To do this, we need to convert the percentage to a decimal by dividing by 100. So, 150% is equal to 1.5. Now, we can multiply 70 by 1.5 to get 105.

Step 2: $=(70)(100 \%+50 \%)$

In this step, Sergei is adding 100% and 50% to get 150%. This is equivalent to adding 1 and 0.5 to get 1.5. Now, we can multiply 70 by 1.5 to get 105.

Step 3: $=(70)(100 \%)+(70)(50 \%)$

In this step, Sergei is multiplying 70 by 100% and 50%. To do this, we need to convert the percentages to decimals. So, 100% is equal to 1 and 50% is equal to 0.5. Now, we can multiply 70 by 1 and 0.5 to get 70 and 35, respectively.

Step 4: $=(70)(1)+(70)\left(\frac{1}{2}\right)$

In this step, Sergei is multiplying 70 by 1 and 0.5. This is equivalent to multiplying 70 by 1 and 1/2. Now, we can add the results to get 70 + 35 = 105.

Step 5: $=70+35$

In this final step, Sergei is adding 70 and 35 to get 105.

Conclusion

In conclusion, Sergei's steps are correct, and the final answer is 105. This problem demonstrates the importance of understanding percentages and how to multiply and add them correctly.

Real-World Applications

Understanding percentages and how to multiply and add them correctly has many real-world applications. For example, in finance, percentages are used to calculate interest rates and investment returns. In business, percentages are used to calculate profit margins and sales growth. In everyday life, percentages are used to calculate tips and discounts.

Tips and Tricks

Here are some tips and tricks to help you understand percentages and how to multiply and add them correctly:

• Always convert percentages to decimals by dividing by 100.
• Use the order of operations (PEMDAS) to multiply and add percentages.
• Break down complex problems into simpler steps.
• Use visual aids, such as diagrams and charts, to help you understand complex concepts.

Common Mistakes

Here are some common mistakes to avoid when working with percentages:

• Not converting percentages to decimals.
• Not following the order of operations (PEMDAS).
• Not breaking down complex problems into simpler steps.
• Not using visual aids to help you understand complex concepts.

Conclusion

In this article, we will answer some of the most frequently asked questions about percentages and how to multiply and add them correctly.

Q: What is a percentage?

A: A percentage is a way to express a value as a fraction of 100. It's denoted by the symbol "%" and is calculated by dividing the value by 100 and multiplying by 100. For example, 25% is equal to 25/100, which can be simplified to 1/4.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, you need to divide the percentage by 100. For example, to convert 25% to a decimal, you would divide 25 by 100, which equals 0.25.

Q: How do I multiply percentages?

A: When multiplying percentages, you need to follow the order of operations (PEMDAS). This means that you need to multiply the numbers first and then add the percentages. For example, if you want to multiply 20% by 30%, you would first convert the percentages to decimals (0.2 and 0.3) and then multiply them together (0.2 x 0.3 = 0.06).

Q: How do I add percentages?

A: When adding percentages, you need to follow the order of operations (PEMDAS). This means that you need to add the percentages first and then multiply the result by the number. For example, if you want to add 20% and 30% to 100, you would first add the percentages (0.2 + 0.3 = 0.5) and then multiply the result by 100 (0.5 x 100 = 50).

Q: What is the difference between a percentage and a decimal?

A: A percentage is a way to express a value as a fraction of 100, while a decimal is a way to express a value as a fraction of 10. For example, 25% is equal to 0.25, which is a decimal.

Q: How do I calculate a percentage of a number?

A: To calculate a percentage of a number, you need to multiply the number by the percentage. For example, if you want to calculate 25% of 100, you would multiply 100 by 0.25 (100 x 0.25 = 25).

Q: How do I calculate a percentage increase or decrease?

A: To calculate a percentage increase or decrease, you need to use the following formula:

Percentage change = (New value - Old value) / Old value x 100

For example, if you want to calculate the percentage increase from 100 to 120, you would use the following formula:

Percentage change = (120 - 100) / 100 x 100 = 20%

Q: What is the difference between a percentage and a ratio?

A: A percentage is a way to express a value as a fraction of 100, while a ratio is a way to express a value as a comparison between two numbers. For example, 2:3 is a ratio, while 66.67% is a percentage.

Q: How do I use percentages in real-world applications?

A: Percentages are used in many real-world applications, such as finance, business, and everyday life. For example, in finance, percentages are used to calculate interest rates and investment returns. In business, percentages are used to calculate profit margins and sales growth. In everyday life, percentages are used to calculate tips and discounts.

Conclusion

In conclusion, understanding percentages and how to multiply and add them correctly is essential in mathematics and real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in working with percentages and achieve success in your academic and professional pursuits.