Evaluate The Expression.\[$(10 \times 7) + (10 - 6) =\$\]

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves simplifying it to a single value. In this article, we will evaluate the expression $(10 \times 7) + (10 - 6)$ using the order of operations (PEMDAS).

Understanding the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. PEMDAS is a popular acronym that stands for:

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.

Evaluating the Expression

Now, let's apply the order of operations to evaluate the expression $(10 \times 7) + (10 - 6)$.

Step 1: Evaluate Expressions Inside Parentheses

The expression inside the first set of parentheses is $10 \times 7$. We will multiply 10 and 7 to get:

$10 \times 7 = 70$

The expression inside the second set of parentheses is $10 - 6$. We will subtract 6 from 10 to get:

$10 - 6 = 4$

Step 2: Evaluate Exponential Expressions (None in this case)

There are no exponential expressions in this problem, so we can move on to the next step.

Step 3: Evaluate Multiplication and Division Operations

We have already evaluated the multiplication operation in the first step, so we can move on to the next step.

Step 4: Evaluate Addition and Subtraction Operations

Now, we will add the results of the two expressions:

$70 + 4 = 74$

Conclusion

In this article, we evaluated the expression $(10 \times 7) + (10 - 6)$ using the order of operations (PEMDAS). We followed the steps of evaluating expressions inside parentheses, exponential expressions, multiplication and division operations, and finally addition and subtraction operations. The final result is 74.

Frequently Asked Questions

• 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 there are multiple operations in an expression. PEMDAS is a popular acronym that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• Q: How do I evaluate an expression using the order of operations? A: To evaluate an expression using the order of operations, follow the steps of evaluating expressions inside parentheses, exponential expressions, multiplication and division operations, and finally addition and subtraction operations.
• Q: What is the final result of the expression $(10 \times 7) + (10 - 6)$? A: The final result of the expression $(10 \times 7) + (10 - 6)$ is 74.

Example Problems

• Evaluate the expression $(5 \times 3) + (8 - 2)$.
• Evaluate the expression $(9 \times 2) + (7 - 1)$.
• Evaluate the expression $(4 \times 6) + (9 - 3)$.

Tips and Tricks

• Always follow the order of operations when evaluating expressions.
• Use parentheses to group expressions and make them easier to evaluate.
• Practice evaluating expressions using the order of operations to become more confident and proficient.

Further Reading

• For more information on the order of operations, visit the Khan Academy website.
• For more practice problems and examples, visit the Mathway website.
• For more information on algebra and mathematics, visit the Wolfram Alpha website.
  

Introduction

In our previous article, we evaluated the expression $(10 \times 7) + (10 - 6)$ using the order of operations (PEMDAS). In this article, we will answer some frequently asked questions about evaluating expressions with the order of operations.

Q&A

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 there are multiple operations in an expression. PEMDAS is a popular acronym that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an expression using the order of operations?

A: To evaluate an expression using the order of operations, follow the steps of evaluating expressions inside parentheses, exponential expressions, multiplication and division operations, and finally addition and subtraction operations.

Q: What is the difference between PEMDAS and BODMAS?

A: PEMDAS and BODMAS are two popular acronyms that stand for the order of operations. PEMDAS is commonly used in the United States, while BODMAS is commonly used in the United Kingdom and other countries. Both acronyms represent the same order of operations:

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: What is the order of operations for fractions?

A: When evaluating expressions with fractions, follow the same order of operations as for whole numbers. However, when simplifying fractions, multiply the numerator and denominator by the same value to eliminate any common factors.

Q: Can I use the order of operations to evaluate expressions with variables?

A: Yes, you can use the order of operations to evaluate expressions with variables. However, when evaluating expressions with variables, make sure to follow the order of operations and simplify the expression as much as possible.

Q: What is the order of operations for exponents?

A: When evaluating expressions with exponents, follow the order of operations and evaluate the exponent first. For example, 2^3 means 2 to the power of 3, which is equal to 8.

Q: Can I use the order of operations to evaluate expressions with decimals?

A: Yes, you can use the order of operations to evaluate expressions with decimals. However, when evaluating expressions with decimals, make sure to follow the order of operations and simplify the expression as much as possible.

Example Problems

• Evaluate the expression $(3 \times 2) + (5 - 1)$.
• Evaluate the expression $(7 \times 3) + (9 - 2)$.
• Evaluate the expression $(4 \times 6) + (8 - 3)$.

Tips and Tricks

• Always follow the order of operations when evaluating expressions.
• Use parentheses to group expressions and make them easier to evaluate.
• Practice evaluating expressions using the order of operations to become more confident and proficient.

Further Reading

• For more information on the order of operations, visit the Khan Academy website.
• For more practice problems and examples, visit the Mathway website.
• For more information on algebra and mathematics, visit the Wolfram Alpha website.

Conclusion

In this article, we answered some frequently asked questions about evaluating expressions with the order of operations. We covered topics such as the order of operations, evaluating expressions with variables, and using the order of operations for fractions and decimals. We also provided example problems and tips and tricks for evaluating expressions using the order of operations.