Calculate The Following Expression:$\[ -80 \% + \frac{54}{50} - 0.25 = \square \\]Enter The Answer As An Exact Decimal Or Simplified Fraction.

Understanding the Expression

The given expression is a combination of a percentage, a fraction, and a decimal. To simplify it, we need to follow the order of operations (PEMDAS):

• Parentheses: None
• Exponents: None
• Multiplication and Division: From left to right
• Addition and Subtraction: From left to right

Breaking Down the Expression

The expression is: $-80 \% + \frac{54}{50} - 0.25$

First, let's convert the percentage to a decimal:

$-80 \% = -\frac{80}{100} = -0.8$

Now, the expression becomes:

$-0.8 + \frac{54}{50} - 0.25$

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 54 and 50 is 2.

$\frac{54}{50} = \frac{54 \div 2}{50 \div 2} = \frac{27}{25}$

Now, the expression becomes:

$-0.8 + \frac{27}{25} - 0.25$

Converting the Fraction to a Decimal

To convert the fraction to a decimal, we can divide the numerator by the denominator:

$\frac{27}{25} = 1.08$

Now, the expression becomes:

$-0.8 + 1.08 - 0.25$

Evaluating the Expression

Now that we have simplified the expression, we can evaluate it by following the order of operations:

1. Add and subtract from left to right:

$-0.8 + 1.08 = 0.28$

$0.28 - 0.25 = 0.03$

The final answer is: 0.03

Conclusion

In this article, we learned how to simplify a complex expression that involves a percentage, a fraction, and a decimal. By following the order of operations and simplifying the fraction, we were able to evaluate the expression and find the final answer.

Tips and Tricks

• When working with percentages, it's often helpful to convert them to decimals to make calculations easier.
• When simplifying fractions, it's essential to find the greatest common divisor (GCD) to reduce the fraction to its simplest form.
• When evaluating expressions, always follow the order of operations (PEMDAS) to ensure accuracy.

Common Mistakes

• Failing to convert percentages to decimals can lead to errors in calculations.
• Not simplifying fractions can make calculations more complicated than necessary.
• Ignoring the order of operations can result in incorrect answers.

Real-World Applications

• Simplifying complex expressions is essential in various fields, such as finance, engineering, and science.
• Understanding the order of operations is crucial in programming and coding.
• Being able to convert between percentages, fractions, and decimals is vital in many real-world applications, such as finance, cooking, and construction.

Further Reading

• For more information on simplifying complex expressions, check out our article on "Simplifying Algebraic Expressions."
• To learn more about the order of operations, visit our article on "Understanding PEMDAS."
• For tips on converting between percentages, fractions, and decimals, read our article on "Converting Between Fractions, Decimals, and Percentages."
  

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order:

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

Q: How do I simplify a fraction?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. We can then divide both the numerator and the denominator by the GCD to simplify the fraction.

For example, let's simplify the fraction 12/16:

1. Find the GCD of 12 and 16: 4
2. Divide both the numerator and the denominator by 4: 12 ÷ 4 = 3, 16 ÷ 4 = 4
3. Simplify the fraction: 3/4

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

A: A percentage is a way of expressing a value as a fraction of 100. For example, 25% is equal to 25/100, which can be simplified to 1/4 or 0.25.

A decimal, on the other hand, is a way of expressing a value as a fraction with a denominator of 10 or a power of 10. For example, 0.25 is equal to 25/100.

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

A: To convert a percentage to a decimal, we can simply divide the percentage by 100:

For example, let's convert 25% to a decimal:

25 ÷ 100 = 0.25

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

A: To convert a decimal to a percentage, we can simply multiply the decimal by 100:

For example, let's convert 0.25 to a percentage:

0.25 × 100 = 25%

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 16 is 4, because 4 is the largest number that divides both 12 and 16 without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers. One way is to list the factors of each number and find the greatest common factor. Another way is to use the Euclidean algorithm.

For example, let's find the GCD of 12 and 16 using the Euclidean algorithm:

1. Divide 16 by 12: 16 = 12 × 1 + 4
2. Divide 12 by 4: 12 = 4 × 3 + 0
3. The remainder is 0, so the GCD is 4

Q: What is the difference between a simplified fraction and a reduced fraction?

A: A simplified fraction is a fraction that has been reduced to its simplest form, meaning that the numerator and denominator have no common factors other than 1. A reduced fraction is a fraction that has been reduced to its simplest form, but may not be in its simplest form.

For example, let's consider the fraction 12/16:

1. Simplify the fraction: 12 ÷ 4 = 3, 16 ÷ 4 = 4, so the simplified fraction is 3/4.
2. Reduce the fraction: 3 and 4 have no common factors other than 1, so the reduced fraction is 3/4.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, we need to follow the order of operations (PEMDAS):

1. Evaluate any expressions inside parentheses first.
2. Evaluate any exponential expressions next.
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

For example, let's evaluate the expression 2 × 3 + 4 - 1:

1. Multiply 2 and 3: 2 × 3 = 6
2. Add 4: 6 + 4 = 10
3. Subtract 1: 10 - 1 = 9

The final answer is: 9