Select All The Expressions That Are Equivalent To 20 % 20\% 20% Of 150.A. 1 25 × 120 \frac{1}{25} \times 120 25 1 ​ × 120 B. 1 4 × 120 \frac{1}{4} \times 120 4 1 ​ × 120 C. 30D. 1 4 ÷ 120 \frac{1}{4} \div 120 4 1 ​ ÷ 120 E. 25

Understanding the Problem

In this problem, we are tasked with identifying expressions that are equivalent to 20% of 150. To begin, let's break down the concept of 20% and how it relates to the number 150. 20% is equivalent to one-fifth or 1/5 of a quantity. Therefore, we need to find expressions that represent one-fifth of 150.

Option A: $\frac{1}{25} \times 120$

At first glance, option A may seem like a viable choice. However, let's examine the expression more closely. The expression $\frac{1}{25} \times 120$ represents one-twenty-fifth of 120, not 150. This means that option A is not equivalent to 20% of 150.

Option B: $\frac{1}{4} \times 120$

Option B represents one-fourth of 120, which is not equivalent to 20% of 150. To see why, let's convert 20% to a decimal: 20% = 0.2. Now, let's calculate 0.2 x 150 = 30. As we can see, option B is not equivalent to 20% of 150.

Option C: 30

Now, let's examine option C, which is the number 30. To determine if this is equivalent to 20% of 150, let's calculate 20% of 150: 0.2 x 150 = 30. As we can see, option C is indeed equivalent to 20% of 150.

Option D: $\frac{1}{4} \div 120$

Option D represents one-fourth divided by 120. To evaluate this expression, we need to follow the order of operations (PEMDAS). First, we divide 1/4 by 120, which is equivalent to multiplying 1/4 by the reciprocal of 120 (1/120). This gives us 1/4 x 1/120 = 1/480. Clearly, option D is not equivalent to 20% of 150.

Option E: 25

Option E is the number 25. To determine if this is equivalent to 20% of 150, let's calculate 20% of 150: 0.2 x 150 = 30. As we can see, option E is not equivalent to 20% of 150.

Conclusion

In conclusion, the only expression that is equivalent to 20% of 150 is option C, which is the number 30. This is because 30 is the result of calculating 20% of 150 (0.2 x 150 = 30). The other options do not meet this criteria and are therefore not equivalent to 20% of 150.

Key Takeaways

• To solve this problem, we need to understand what 20% means and how it relates to the number 150.
• We need to evaluate each option and determine if it is equivalent to 20% of 150.
• The correct answer is option C, which is the number 30.

Additional Tips and Tricks

• When working with percentages, it's essential to convert them to decimals to make calculations easier.
• To calculate a percentage of a number, multiply the decimal equivalent of the percentage by the number.
• When evaluating expressions, follow the order of operations (PEMDAS) to ensure that calculations are performed correctly.

Real-World Applications

• Understanding percentages and how to calculate them is essential in various real-world applications, such as finance, business, and science.
• Being able to identify equivalent expressions is a valuable skill that can be applied to a wide range of problems.

Common Mistakes to Avoid

• When working with percentages, it's easy to get confused between different percentages or to make calculation errors.
• To avoid these mistakes, make sure to double-check your calculations and use a calculator when necessary.

Conclusion

Q: What is the definition of 20%?

A: 20% is equivalent to one-fifth or 1/5 of a quantity. It can also be represented as 0.2 in decimal form.

Q: How do I calculate 20% of a number?

A: To calculate 20% of a number, multiply the decimal equivalent of 20% (0.2) by the number. For example, to calculate 20% of 150, multiply 0.2 by 150: 0.2 x 150 = 30.

Q: What is the difference between 20% and 25%?

A: 20% is equivalent to one-fifth or 1/5 of a quantity, while 25% is equivalent to one-fourth or 1/4 of a quantity. To calculate 25% of a number, multiply the decimal equivalent of 25% (0.25) by the number.

Q: Can I use a calculator to calculate 20% of a number?

A: Yes, you can use a calculator to calculate 20% of a number. Simply enter the number and multiply it by 0.2 to get the result.

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

A: To convert a percentage to a decimal, divide the percentage by 100. For example, to convert 20% to a decimal, divide 20 by 100: 20 ÷ 100 = 0.2.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it essential to follow the order of operations (PEMDAS)?

A: Following the order of operations (PEMDAS) ensures that mathematical expressions are evaluated correctly and consistently. It helps to avoid errors and confusion when working with complex expressions.

Q: Can I use a calculator to evaluate expressions that involve percentages?

A: Yes, you can use a calculator to evaluate expressions that involve percentages. Simply enter the expression and the calculator will perform the necessary calculations.

Q: What are some common mistakes to avoid when working with percentages?

A: Some common mistakes to avoid when working with percentages include:

• Confusing different percentages or calculation errors
• Failing to convert percentages to decimals
• Not following the order of operations (PEMDAS)
• Not double-checking calculations

Q: How can I practice working with percentages?

A: You can practice working with percentages by:

• Calculating percentages of numbers
• Converting percentages to decimals
• Evaluating expressions that involve percentages
• Solving problems that involve percentages

Conclusion

In conclusion, working with percentages requires a solid understanding of the concept and how to calculate them. By following the steps outlined in this article and practicing regularly, you can become proficient in working with percentages and avoid common mistakes. Remember to always double-check your calculations and use a calculator when necessary.