Do you often find yourself scratching your head when faced with complex mathematical calculations? Fear not, for we have created a simple step-by-step guide to solve the perplexing equation 10-10×10+10. In this article, we will break down the problem into manageable chunks, providing you with the tools and understanding to conquer similar equations with ease.

Mathematics can be a daunting subject, even for the most astute minds. Equations like 10-10×10+10 may seem overwhelming at first glance, but with the right approach, they can be demystified. By following our step-by-step guide, you will gain a clearer understanding of the underlying principles at play, empowering you to solve not only this specific equation but also other equations of comparable complexity. Let’s dive in and unravel the secrets of solving 10-10×10+10!

Understanding the Order of Operations

The Order of Operations is a crucial concept in mathematics that ensures consistent and unambiguous interpretation of expressions. It provides a set of rules to determine the priority in which different operations should be performed within an equation. By following the Order of Operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), one can solve complex mathematical problems accurately and avoid confusion.

A. Explanation of PEMDAS acronym

The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. These operations must be performed in the specified order to obtain the correct solution.

The first priority is given to parentheses. If an equation contains parentheses, the expression inside them should be evaluated first. Parentheses allow the isolation and evaluation of specific parts of an equation, and their removal simplifies the problem.

B. Emphasize the significance of following this order

Following the Order of Operations is crucial because it ensures consistent and predictable outcomes when solving mathematical problems. Without adhering to this order, the solution to an equation may vary depending on the interpretation, leading to incorrect results.

By consistently applying the Order of Operations, mathematicians, scientists, and engineers can communicate and share their findings accurately. It also enables students to solve math problems step-by-step, building a solid foundation for more advanced mathematical concepts.

Understanding and correctly implementing the Order of Operations is necessary not only for academic purposes but also in everyday life. For example, when calculating bills or budgeting expenses, following the correct order ensures accurate calculations and prevents potentially costly errors.

In summary, understanding the Order of Operations is fundamental in solving mathematical problems correctly. Following the rules outlined by PEMDAS guarantees consistent results and builds a strong mathematical foundation. By mastering this concept, individuals can solve complex equations accurately and confidently navigate various real-life situations where mathematical calculations are required.

## Step 1: Identify & Eliminate Parentheses

### A. Explaining the absence of parentheses in the given problem

In the problem 10-10×10+10, there are no parentheses present. Parentheses are commonly used in mathematical expressions to indicate a different order of operations within a larger equation. In this case, the absence of parentheses simplifies the problem as it allows us to follow a more straightforward order of operations.

### B. Providing examples with parentheses to exhibit the process if they were present

To better understand the role of parentheses and their impact on the order of operations, let’s consider an example with parentheses. Suppose we have the expression: 10 – (2 + 3) x 2. In this case, the parentheses indicate that the addition operation should be performed before the multiplication.

To solve this example, we would start by evaluating the expression within the parentheses: 2 + 3 = 5.

Afterward, we proceed with the multiplication: 5 x 2 = 10.

Finally, we subtract 10 from the original number, 10, resulting in 0 as the final answer.

This example demonstrates how the presence of parentheses can alter the sequence of calculations. However, in the given problem of 10-10×10+10, there are no parentheses present. Therefore, we can move on to the next step of the order of operations.

By understanding the concept of parentheses and their effect on mathematical expressions, you will be better equipped to handle more complex problems involving multiple sets of parentheses. However, in this particular case, the absence of parentheses simplifies the calculations, making it easier to proceed to the following steps of the order of operations.

Remember, when working with expressions that contain parentheses, it is crucial to always evaluate the operations within the parentheses first, before moving on to other parts of the equation. Without parentheses present, we can focus on the next step in solving the problem: evaluating exponents.

IStep 2: Evaluate Exponents

## Explanation of Exponents

Exponents are a way to represent repeated multiplication. An exponent is a small number written above and to the right of a number, called a base, and it indicates how many times the base should be multiplied by itself.

For example, in the expression 2^3, the base is 2 and the exponent is 3. This means that 2 should be multiplied by itself 3 times: 2 x 2 x 2 = 8.

### Example:

If we had the expression 5^2, the base is 5 and the exponent is 2. Therefore, we need to multiply 5 by itself 2 times, resulting in 5 x 5 = 25.

It is important to note that the given problem, 10-10×10+10, does not contain any exponents. Exponents are not a part of this expression, so we can move on to the next step in solving it.

## Step 3 – Perform Multiplication and Division, from left to right

### A. Explanation of the multiplication and division rules

In order to correctly solve mathematical expressions, it is crucial to understand the rules for multiplication and division. These operations should be performed from left to right, meaning that the calculations should be carried out in the order they appear in the expression. Multiplication is denoted by the symbol “*”, while division is denoted by “/”.

### B. Walking through the calculations and providing the correct answer

Now that we have successfully eliminated parentheses and assessed any exponents in the given expression “10-10×10+10,” it is time to move on to the next step: performing multiplication and division.

Following the order of operations, we first look for any multiplication or division operations from left to right. In this case, we have one multiplication operation: 10 multiplied by 10.

10 x 10 = 100

Now that we have performed the multiplication, we rewrite the expression using the calculated value:

10 – 100 + 10

Moving on, we need to perform the remaining addition and subtraction operations from left to right.

10 – 100 = -90

Now, we rewrite the expression using the intermediate result:

-90 + 10

Finally, we perform the addition:

-90 + 10 = -80

Therefore, the correct solution for the expression 10-10×10+10 is -80.

It is important to note that in cases where there are multiple multiplication or division operations, performing them from left to right ensures that we obtain the correct result. Failing to follow this order may lead to errors and incorrect solutions.

By applying the multiplication and division rules correctly, we have successfully solved the given expression. Moving forward, we will now proceed to the next step: performing addition and subtraction.

## Step 4: Perform Addition and Subtraction, from left to right

### A. Clarification of the addition and subtraction rules

In this step, we will focus on performing addition and subtraction operations from left to right. It is important to note that addition and subtraction have the same precedence and should be done in the order they appear.

When performing addition, we simply combine two or more numbers to obtain a single sum. For example, 5 + 3 equals 8. Addition is commutative, meaning that the order of the numbers does not affect the result. Therefore, 3 + 5 also equals 8.

Subtraction, on the other hand, involves subtracting a number from another. For instance, when subtracting 3 from 7, we get 4. Unlike addition, subtraction is not commutative. In other words, the order of the numbers does matter. For example, 7 – 3 is not the same as 3 – 7.

### B. Executing the operations to obtain the final result

In our problem, 10 – 10 × 10 + 10, we will perform the operations in the order they appear from left to right.

First, we start with 10 – 10, which equals 0. Next, we multiply 0 by 10, resulting in 0. Finally, we add 10 to 0, giving us a final answer of 10.

To summarize, the correct solution to the problem 10 – 10 × 10 + 10 is 10. It is essential to follow the order of operations and perform addition and subtraction operations in the order they appear to arrive at the right result.

It is worth noting that many people make the mistake of performing addition and subtraction before multiplication and division, which leads to incorrect results. By understanding and applying the order of operations correctly, you can avoid such errors and solve mathematical problems accurately.

Remember to take your time, double-check each step, and follow the order of operations diligently. Practice solving similar problems to reinforce your understanding of this fundamental concept in mathematics.

In the next section, we will apply the order of operations to the original problem, recapping the rules of PEMDAS and providing a step-by-step solution for a comprehensive understanding.

VApplying the Order of Operations to the Original Problem

## Recapping the rules of PEMDAS

Before applying the order of operations to the original problem of 10-10×10+10, it is crucial to recap the rules of PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. These rules help ensure that mathematical calculations are performed correctly and consistently.

### Parentheses

The first step in the order of operations is to identify and eliminate parentheses. However, in the given problem of 10-10×10+10, there are no parentheses present.

### Exponents

The next step, which involves evaluating any exponents, is not applicable in this problem. There are no exponents to consider.

### Multiplication and Division

After parentheses and exponents, the order of operations dictates that multiplication and division should be performed from left to right.

Multiplication involves multiplying two numbers together, while division involves dividing one number by another. To illustrate this step, let’s consider a similar example with parentheses: (2+3) x 4 ÷ 2.

First, we solve the expression inside the parentheses, which evaluates to 5. Then, we proceed with the multiplication and division from left to right.

(2+3) x 4 ÷ 2 = 5 x 4 ÷ 2

= 20 ÷ 2

= 10

In the original problem, we have 10-10×10+10. Following the same principle, we complete the multiplication before moving on to the next step.

10-10×10+10 = 10 – 100 + 10

### Addition and Subtraction

Finally, the last step is to perform addition and subtraction from left to right.

Using the result from the previous step, we continue with the addition and subtraction:

10 – 100 + 10 = -90 + 10 = -80

By following the order of operations correctly, we find that the value of 10-10×10+10 is -80.

To summarize, applying the order of operations (PEMDAS) to the original problem involves performing multiplication and division from left to right, followed by addition and subtraction from left to right.

Remembering and applying these rules correctly is crucial to solving mathematical problems accurately and consistently.

## VIDetailed Step-by-Step Solution

### A. Breaking down the original problem using the steps explained earlier

To solve the problem 10-10×10+10 in a step-by-step manner, we will follow the rules of the order of operations, which is represented by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

### B. Presenting each step with detailed calculations, highlighting intermediate results

Step 1: Identify & Eliminate Parentheses

Since there are no parentheses in the given problem 10-10×10+10, we can proceed to the next step.

Step 2: Evaluate Exponents

Similarly, there are no exponents present in the problem, so we move on to the next step.

Step 3: Perform Multiplication and Division, from left to right

Following the left-to-right rule, we first perform the multiplication operation: 10×10 = 100.

Step 4: Perform Addition and Subtraction, from left to right

Continuing with the left-to-right rule, we have 10-100+10. Subtracting 100 from 10 gives us -90, and adding 10 to -90 results in -80.

By applying the order of operations, we have successfully solved the problem step by step. The final answer is -80.

It is important to carefully follow the order of operations to arrive at the correct solution for any mathematical expression. Failing to do so can lead to incorrect results.

Throughout this detailed step-by-step solution, it is evident that the order in which the operations are performed plays a crucial role. By correctly following the order of operations, we ensure that each mathematical expression is evaluated accurately.

Remembering to evaluate parentheses first (if present), followed by exponents, and proceeding with multiplication and division from left to right, and finally performing addition and subtraction from left to right is essential.

In complex mathematical expressions, the order of operations ensures that each operation is performed in a logical and systematic manner, preventing confusion and ambiguity.

To solidify your understanding of the order of operations, it is recommended to practice solving similar problems and applying the concepts discussed in this article. Through practice, you will become more comfortable and proficient in correctly solving mathematical expressions.

## Common Errors to Avoid

### A. Identifying typical mistakes people make when solving similar problems

When solving problems that involve the order of operations, such as 10-10×10+10, it is common for people to make certain errors. One common mistake is ignoring the order of operations and performing the operations from left to right without considering multiplication and division before addition and subtraction. For example, some may incorrectly solve the problem as 10-100+10, resulting in an incorrect answer of -80.

Another error is disregarding the rule of performing multiplication and division before addition and subtraction, but within each operation, performing them from left to right. This can lead to incorrect answers as the order of operations is not followed correctly. For instance, some might incorrectly solve the problem as -10×100+10, resulting in an incorrect answer of -990.

Additionally, mistakes may occur when combining multiple operations in a single step without following the order of operations. For example, some might incorrectly solve the problem as -10×100-10, without first resolving the multiplication, resulting in an incorrect answer of -1000.

### B. Providing tips and suggestions to prevent these errors

To avoid these common errors, it is crucial to remember and follow the order of operations correctly. One helpful tip is to use parentheses to explicitly indicate which operations should be performed first. By using parentheses, it becomes less likely to mistakenly perform addition or subtraction before multiplication or division.

Another tip is to approach the problem step by step, following the order of operations rigorously. By mentally breaking down the problem into smaller parts and resolving each part according to the rules of PEMDAS, it becomes easier to avoid errors.

Furthermore, it is crucial to double-check the calculations and intermediate results at each step. This can help catch any mistakes early on before they compound as the calculations progress. Taking the time to verify the calculations ensures accuracy in the final answer.

Practicing similar problems regularly can also help in familiarizing oneself with the correct application of the order of operations. By doing so, the rules and their correct implementation become more intuitive and errors are less likely to occur.

By being aware of these common errors and following the provided tips and suggestions, one can significantly improve their problem-solving skills and avoid making mistakes when solving similar problems that involve the order of operations.

## X. Alternative Notations and Solutions

### A. Discussing alternative notations or variations of the problem

In addition to the standard notation of 10-10×10+10, there can be variations or alternative notations that can lead to different interpretations of the problem. It is important to be aware of these variations and understand the potential differences in their solutions.

One common alternative notation is the use of brackets instead of parentheses. For example, the expression [10-10]x10+10 could be seen as different from 10-[10×10]+10. In the former case, the brackets indicate that the subtraction should be performed before the multiplication, resulting in a different solution compared to the original expression. It is crucial to pay attention to the grouping symbols used and understand their impact on the order of operations.

Another variation that can be encountered is the omission of multiplication symbols between numbers or parentheses. For instance, the expression 10(10) can be interpreted differently based on whether it is seen as multiplication or a mere adjacent placement of numbers. This omission can cause confusion and lead to incorrect solutions if not understood correctly.

### B. Providing examples and explaining how the steps would differ in those cases

To illustrate the impact of alternative notations or variations, let’s consider the expression 10-10×10+10 in relation to the examples discussed earlier.

If the expression is written as [10-10]x10+10, the first step would involve performing the subtraction within the brackets, resulting in 0x10+10. The subsequent steps would follow the same order of operations, performing the multiplication first and then the addition, resulting in the final answer: 0+10=10.

On the other hand, if the expression is written as 10-[10×10]+10, the first step would involve performing the multiplication within the parentheses, resulting in 10-100+10. Following the order of operations, the subtraction comes next, resulting in -90+10. Finally, the addition is performed, giving us the final solution: -90+10=-80.

As demonstrated by these examples, alternative notations or variations can significantly affect the solution to the problem. It is essential to carefully consider the grouping symbols used and the implied operations when encountering these variations.

By being aware of alternative notations and understanding their impact on the order of operations, individuals can avoid making errors and arrive at the correct solutions for a wide range of math problems. Familiarity with these variations enhances mathematical proficiency and ensures accurate problem-solving.

## RecommendedPractical Application and Real-Life Examples

### A. Demonstrating scenarios where understanding the order of operations is crucial

Understanding the order of operations is not only important for solving mathematical equations correctly, but it also has real-life applications. Here are a few scenarios where knowing the correct order of operations is crucial:

1. DIY Projects: When working on do-it-yourself projects that involve measurements and calculations, such as cutting materials for a home renovation, following the correct order of operations ensures accurate results. Failing to do so can lead to errors, wasted materials, and additional costs.

2. Cooking and Baking: Cooking and baking recipes often involve measurements, conversions, and calculations. Following the order of operations is essential to ensure the right proportions of ingredients, cooking times, and temperatures. Making a mistake in the order of operations can result in a disastrous culinary outcome.

3. Budgeting and Finances: Managing personal or business finances requires careful calculations. Whether it’s budgeting monthly expenses or calculating compound interest on loans, understanding the order of operations ensures accurate calculations, helping individuals make informed financial decisions.

### B. Illustrating real-life examples to emphasize the relevance of the article’s content

To further emphasize the relevance of understanding the order of operations, let’s consider a couple of real-life examples:

1. Shopping Discounts: Imagine you are planning to take advantage of a 30% discount on a $100 item. To calculate the final price, you need to multiply the original price by 0.3 and then subtract that result from the original price. If you incorrectly add the discount to the original price, you may find yourself paying more than expected.

2. Time Management: Suppose you have a busy schedule with multiple tasks to complete. Understanding the order of operations allows you to prioritize and organize your tasks effectively. By following a logical order, you can ensure that important tasks are completed first and avoid wasting time and energy on less critical ones.

By providing these practical examples, it becomes evident that understanding the order of operations is far from being limited to mathematics alone. This knowledge is essential for various real-life situations, helping individuals make accurate calculations and decisions in everyday scenarios.

In conclusion, the eleventh section of this article has highlighted the practical application and relevance of understanding the order of operations. By demonstrating scenarios where this knowledge is crucial and providing real-life examples, readers are encouraged to appreciate the significance of mastering the correct order of operations in their day-to-day lives.

## XConclusion

In conclusion, understanding the order of operations is crucial for solving mathematical expressions correctly. This article has provided a step-by-step guide to solving the problem 10-10×10+10 using the PEMDAS acronym. By following the rules of Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction in the correct order, readers can confidently solve similar problems without confusion or errors.

Throughout this guide, we have emphasized that following the order of operations is significant because it ensures consistency and accuracy in mathematical calculations. By eliminating parentheses, evaluating exponents, performing multiplication and division from left to right, and then performing addition and subtraction from left to right, readers can prevent errors and obtain the correct solutions.

To reinforce the concepts discussed, we have presented a detailed step-by-step solution to the original problem. We broke down the problem using the steps explained earlier and provided calculations, highlighting intermediate results. This approach allows readers to understand the logical progression of the solution process.

Additionally, we have identified common errors to avoid when solving similar problems. By recognizing these mistakes and implementing the provided tips and suggestions, readers can enhance their problem-solving skills and avoid unnecessary errors.

Furthermore, we have touched on alternative notations and solutions, acknowledging that mathematical expressions can be presented differently. Through examples and explanations, readers can grasp how the steps of the order of operations would differ in these alternative cases.

To emphasize the relevance of this topic in real-life scenarios, we have demonstrated practical applications where understanding the order of operations is crucial. By showcasing real-life examples, such as interpreting financial statements or designing blueprints, we have shown readers that the knowledge gained from this article is practical and applicable beyond the realm of a math classroom.

In conclusion, we encourage readers to practice and apply the knowledge they have gained from this comprehensive article. By doing so, they will become more confident and proficient in solving mathematical problems correctly, benefiting their academic and professional pursuits that involve mathematical calculations.