Simplify The Expression:$\frac{5}{2}(8)-2$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. In this article, we will focus on simplifying the expression $\frac{5}{2}(8)-2$. We will break down the problem into smaller steps, and by the end of this article, you will understand how to simplify this expression.

Understanding the Expression

The given expression is $\frac{5}{2}(8)-2$. To simplify this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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.

Step 1: Multiply $\frac{5}{2}$ and 8

The first step is to multiply $\frac{5}{2}$ and 8. To do this, we multiply the numerator (5) and the denominator (2) by 8.

$\frac{5}{2}(8) = \frac{5 \times 8}{2}$

Now, we can simplify the expression by multiplying 5 and 8.

$\frac{5 \times 8}{2} = \frac{40}{2}$

Step 2: Simplify the Fraction

The fraction $\frac{40}{2}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

$\frac{40}{2} = \frac{40 \div 2}{2 \div 2} = \frac{20}{1}$

Step 3: Subtract 2

Now that we have simplified the fraction, we can subtract 2 from the result.

$\frac{20}{1} - 2 = 20 - 2 = 18$

Conclusion

In this article, we simplified the expression $\frac{5}{2}(8)-2$ by following the order of operations (PEMDAS). We multiplied $\frac{5}{2}$ and 8, simplified the fraction, and finally subtracted 2 from the result. By the end of this article, you should have a clear understanding of how to simplify this expression.

Tips and Variations

• When simplifying expressions, always follow the order of operations (PEMDAS).
• When multiplying fractions, multiply the numerators and denominators separately.
• When subtracting a whole number from a fraction, convert the whole number to a fraction with the same denominator.

Practice Problems

Try simplifying the following expressions:

1. $\frac{3}{4}(12)-3$
2. $\frac{2}{3}(9)+2$
3. $\frac{5}{6}(18)-5$

Common Mistakes

• Failing to follow the order of operations (PEMDAS).
• Not simplifying fractions before performing operations.
• Not converting whole numbers to fractions with the same denominator.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. For example, in finance, simplifying expressions can help you calculate interest rates and investment returns. In science, simplifying expressions can help you model complex systems and make predictions.

Conclusion

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Introduction

In our previous article, we simplified the expression $\frac{5}{2}(8)-2$ by following the order of operations (PEMDAS). In this article, we will answer some common questions related to simplifying expressions and provide additional tips and examples.

Q&A

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying expressions. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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 fractions?

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

Q: What is the difference between multiplying and dividing fractions?

A: When multiplying fractions, you multiply the numerators and denominators separately. When dividing fractions, you invert the second fraction (i.e., flip the numerator and denominator) and then multiply.

Q: Can I simplify expressions with variables?

A: Yes, you can simplify expressions with variables. However, you need to follow the order of operations (PEMDAS) and simplify the expression as if the variables were numbers.

Q: How do I handle negative numbers when simplifying expressions?

A: When simplifying expressions with negative numbers, you need to follow the order of operations (PEMDAS) and simplify the expression as if the negative numbers were positive. Then, apply the rules for negative numbers (e.g., multiplying two negative numbers gives a positive result).

Q: Can I use a calculator to simplify expressions?

A: Yes, you can use a calculator to simplify expressions. However, it's essential to understand the underlying math and be able to simplify expressions without a calculator.

Tips and Examples

• When simplifying expressions, always follow the order of operations (PEMDAS).
• When multiplying fractions, multiply the numerators and denominators separately.
• When dividing fractions, invert the second fraction (i.e., flip the numerator and denominator) and then multiply.
• When simplifying expressions with variables, treat the variables as if they were numbers.
• When handling negative numbers, follow the order of operations (PEMDAS) and apply the rules for negative numbers.

Practice Problems

Try simplifying the following expressions:

1. $\frac{3}{4}(12)-3$
2. $\frac{2}{3}(9)+2$
3. $\frac{5}{6}(18)-5$
4. $2x^2 + 3x - 4$
5. $-3x^2 + 2x + 1$

Common Mistakes

• Failing to follow the order of operations (PEMDAS).
• Not simplifying fractions before performing operations.
• Not converting whole numbers to fractions with the same denominator.
• Not handling negative numbers correctly.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. For example, in finance, simplifying expressions can help you calculate interest rates and investment returns. In science, simplifying expressions can help you model complex systems and make predictions.

Conclusion

In conclusion, simplifying expressions is a fundamental skill in mathematics that requires following the order of operations (PEMDAS) and simplifying fractions. By understanding the rules and examples provided in this article, you will be able to simplify expressions with confidence and tackle more complex problems.