Calculate The Value Of $2 \cdot (10.5 - 1.5)$.

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Introduction

In mathematics, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In this article, we will calculate the value of $2 \cdot (10.5 - 1.5)$ using the order of operations.

Understanding the Expression

The given expression is $2 \cdot (10.5 - 1.5)$. To calculate the value of this expression, we need to follow the order of operations.

The expression contains two operations: subtraction and multiplication. The subtraction operation is inside the parentheses, and the multiplication operation is outside the parentheses.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is $10.5 - 1.5$. To evaluate this expression, we need to subtract 1.5 from 10.5.

# Evaluate the expression inside the parentheses
expression_inside_parentheses = 10.5 - 1.5
print(expression_inside_parentheses)

Step 2: Multiply 2 by the Result

After evaluating the expression inside the parentheses, we get the result 9.0. Now, we need to multiply 2 by this result.

# Multiply 2 by the result
result = 2 * expression_inside_parentheses
print(result)

Conclusion

In this article, we calculated the value of $2 \cdot (10.5 - 1.5)$ using the order of operations. We first evaluated the expression inside the parentheses, and then multiplied 2 by the result.

The final answer is 18.0\boxed{18.0}.

Frequently Asked Questions

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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

A: To evaluate an expression with multiple operations, you need to follow the order of operations. First, evaluate the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the result of $2 \cdot (10.5 - 1.5)$?

A: The result of $2 \cdot (10.5 - 1.5)$ is 18.0.

Further Reading

If you want to learn more about the order of operations, I recommend checking out the following resources:

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Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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

A: To evaluate an expression with multiple operations, you need to follow the order of operations. First, evaluate the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the result of $2 \cdot (10.5 - 1.5)$?

A: The result of $2 \cdot (10.5 - 1.5)$ is 18.0.

Q: Why do I need to follow the order of operations?

A: Following the order of operations is important because it ensures that mathematical expressions are evaluated consistently and accurately. If you don't follow the order of operations, you may get different results depending on the order in which you perform the operations.

Q: Can I use a calculator to evaluate the expression $2 \cdot (10.5 - 1.5)$?

A: Yes, you can use a calculator to evaluate the expression $2 \cdot (10.5 - 1.5)$. However, it's still important to understand the order of operations and how to evaluate the expression manually.

Q: How do I evaluate an expression with negative numbers?

A: To evaluate an expression with negative numbers, you need to follow the same order of operations as before. However, when you encounter a negative number, you need to remember that it is the opposite of the positive number. For example, -3 is the opposite of 3.

Q: Can I use a calculator to evaluate an expression with negative numbers?

A: Yes, you can use a calculator to evaluate an expression with negative numbers. However, it's still important to understand how to evaluate the expression manually and to remember that negative numbers are the opposite of positive numbers.

Q: How do I evaluate an expression with decimals?

A: To evaluate an expression with decimals, you need to follow the same order of operations as before. However, when you encounter a decimal number, you need to remember that it is a fraction of a whole number. For example, 0.5 is equal to 1/2.

Q: Can I use a calculator to evaluate an expression with decimals?

A: Yes, you can use a calculator to evaluate an expression with decimals. However, it's still important to understand how to evaluate the expression manually and to remember that decimal numbers are fractions of whole numbers.

Q: What is the difference between $2 \cdot (10.5 - 1.5)$ and $2 \cdot (1.5 - 10.5)$?

A: The difference between $2 \cdot (10.5 - 1.5)$ and $2 \cdot (1.5 - 10.5)$ is the order in which the operations are performed. In the first expression, the subtraction operation is performed first, and then the multiplication operation is performed. In the second expression, the subtraction operation is performed in the opposite order, and then the multiplication operation is performed.

Q: How do I evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, you need to follow the order of operations. First, evaluate the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to evaluate an expression with parentheses?

A: Yes, you can use a calculator to evaluate an expression with parentheses. However, it's still important to understand how to evaluate the expression manually and to remember that parentheses indicate the order in which operations should be performed.

Q: What is the result of $2 \cdot (10.5 - 1.5) + 3$?

A: The result of $2 \cdot (10.5 - 1.5) + 3$ is 21.0.

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

A: To evaluate an expression with multiple operations and parentheses, you need to follow the order of operations. First, evaluate the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to evaluate an expression with multiple operations and parentheses?

A: Yes, you can use a calculator to evaluate an expression with multiple operations and parentheses. However, it's still important to understand how to evaluate the expression manually and to remember that parentheses indicate the order in which operations should be performed.

Q: What is the result of $2 \cdot (10.5 - 1.5) + 3 - 2$?

A: The result of $2 \cdot (10.5 - 1.5) + 3 - 2$ is 19.0.

Q: How do I evaluate an expression with multiple operations, parentheses, and negative numbers?

A: To evaluate an expression with multiple operations, parentheses, and negative numbers, you need to follow the order of operations. First, evaluate the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to evaluate an expression with multiple operations, parentheses, and negative numbers?

A: Yes, you can use a calculator to evaluate an expression with multiple operations, parentheses, and negative numbers. However, it's still important to understand how to evaluate the expression manually and to remember that parentheses indicate the order in which operations should be performed.

Q: What is the result of $2 \cdot (10.5 - 1.5) + 3 - 2 - 1$?

A: The result of $2 \cdot (10.5 - 1.5) + 3 - 2 - 1$ is 17.0.

Q: How do I evaluate an expression with multiple operations, parentheses, and decimal numbers?

A: To evaluate an expression with multiple operations, parentheses, and decimal numbers, you need to follow the order of operations. First, evaluate the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to evaluate an expression with multiple operations, parentheses, and decimal numbers?

A: Yes, you can use a calculator to evaluate an expression with multiple operations, parentheses, and decimal numbers. However, it's still important to understand how to evaluate the expression manually and to remember that parentheses indicate the order in which operations should be performed.

Q: What is the result of $2 \cdot (10.5 - 1.5) + 3 - 2 + 0.5$?

A: The result of $2 \cdot (10.5 - 1.5) + 3 - 2 + 0.5$ is 18.5.

Q: How do I evaluate an expression with multiple operations, parentheses, and mixed numbers?

A: To evaluate an expression with multiple operations, parentheses, and mixed numbers, you need to follow the order of operations. First, evaluate the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to evaluate an expression with multiple operations, parentheses, and mixed numbers?

A: Yes, you can use a calculator to evaluate an expression with multiple operations, parentheses, and mixed numbers. However, it's still important to understand how to evaluate the expression manually and to remember that parentheses indicate the order in which operations should be performed.

Q: What is the result of $2 \cdot (10.5 - 1.5) + 3 - 2 + 1\frac{1}{2}$?

A: The result of $2 \cdot (10.5 - 1.5) + 3 - 2 + 1\frac{1}{2}$ is 20.5.

Q: How do I evaluate an expression with multiple operations, parentheses, and fractions?

A: To evaluate an expression with multiple operations, parentheses, and fractions, you need to follow the order of operations. First, evaluate the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to evaluate an expression with multiple operations, parentheses, and fractions?

A: Yes, you can use a calculator to evaluate an expression with multiple operations, parentheses, and fractions. However, it's still important to understand how to