Solve 1 - 61 + 151: Step-by-Step Calculation
Let's break down how to solve the arithmetic problem 1 - 61 + 151. It's a straightforward calculation, but going through it step by step ensures accuracy and understanding. So, grab your mental calculator, and let’s get started!
Step 1: Understanding the Expression
At its heart, we have a simple arithmetic expression involving integers. The expression 1 - 61 + 151 consists of three numbers and two operators: subtraction and addition. To solve this correctly, we need to follow the proper order of operations. In this case, since we only have addition and subtraction, we perform the operations from left to right.
Keywords: Arithmetic expression, integers, subtraction, addition, order of operations.
The key thing to remember is to treat this as a sequence of actions. We start with 1, then we subtract 61 from it, and finally, we add 151 to the result. Thinking of it this way helps avoid confusion and ensures that we don't accidentally add before subtracting or vice versa. Many people find it helpful to rewrite the expression with parentheses to emphasize the order: (1 - 61) + 151. This doesn't change the math, but it visually reinforces the sequence of operations. By understanding this fundamental principle, we set ourselves up for accurately solving the problem. The order in which you perform these calculations matters, especially when more complex expressions are involved. For now, keeping it simple and going from left to right will do the trick perfectly. This methodical approach is crucial, particularly when dealing with more complex calculations. Make sure each step is clear before moving on.
Step 2: Performing the First Operation (1 - 61)
The first operation we need to tackle is 1 - 61. This is where we subtract 61 from 1. Now, since 61 is larger than 1, the result will be a negative number. Think of it like starting with one dollar and then owing someone 61 dollars. You'd be in debt!
Keywords: Subtraction, negative number, debt, integers.
Mathematically, 1 - 61 = -60. If you're not immediately comfortable with negative numbers, it can be helpful to visualize a number line. Start at 1 on the number line, and then move 61 spaces to the left. You'll end up at -60. Another way to think about it is to recognize that 61 - 1 = 60, and then simply apply the negative sign since we're subtracting a larger number from a smaller one. Understanding how to handle negative numbers is crucial for more complex calculations. Practicing with number lines and real-world examples, like owing money, can make the concept more intuitive. Remember, negative numbers are just as valid and real as positive numbers; they simply represent values less than zero. This step provides the intermediate result that sets the stage for the final calculation. Mastering operations with negative numbers is not only beneficial for this particular problem, but it's also a valuable skill for various mathematical and real-world applications.
Step 3: Performing the Second Operation (-60 + 151)
Now that we've completed the first operation, we have -60 + 151. This means we need to add 151 to -60. Essentially, we are starting at -60 on the number line and moving 151 spaces to the right.
Keywords: Addition, number line, positive result, integers.
To solve this, we can think of it as finding the difference between 151 and 60, and then keeping the sign of the larger number. In other words, 151 - 60 = 91. Since 151 is positive and larger than 60, our result will be positive. Therefore, -60 + 151 = 91. Another way to visualize this is to imagine you owe someone $60, but then you receive $151. After paying off your debt, you would have $91 left over. This real-world analogy can make the addition of positive and negative numbers more intuitive. The positive result indicates that 151 outweighs the negative impact of -60. This calculation is a great demonstration of how addition and subtraction interact with negative numbers, highlighting the importance of understanding both the magnitude and the sign of each number. Make sure you are comfortable with these types of operations before moving on to more complex problems. The careful execution of this step ensures an accurate final answer.
Step 4: The Final Answer
After performing both operations, we arrive at our final answer. 1 - 61 + 151 = 91. So, the solution to the expression is 91.
Keywords: Solution, arithmetic, final answer, integers.
That’s it! By breaking down the problem into smaller, manageable steps, we were able to solve it accurately. Remember, always follow the order of operations (from left to right for addition and subtraction) and pay close attention to the signs of the numbers. Whether you’re dealing with simple arithmetic or more complex mathematical problems, a systematic approach will always lead you to the correct solution. Keep practicing, and you'll become a pro in no time! This problem serves as a great example of how breaking down calculations into manageable steps can help in achieving accurate solutions. Always remember the importance of order of operations and careful consideration of the signs of the numbers involved. With practice, problems like these become second nature, laying a solid foundation for tackling more complex mathematical challenges. This final calculation emphasizes the significance of careful execution in mathematics.
Tips for Avoiding Errors
- Double-Check Your Work: Always take a moment to review your calculations to ensure you haven't made any simple mistakes.
- Use a Number Line: Visual aids like a number line can be extremely helpful, especially when dealing with negative numbers.
- Break Down Complex Problems: If the expression seems overwhelming, break it down into smaller, more manageable parts.
- Practice Regularly: The more you practice, the more comfortable you'll become with arithmetic operations.
Conclusion
We've successfully calculated 1 - 61 + 151 by following a step-by-step approach. Remember, understanding the basics and taking your time are key to mastering arithmetic. Keep practicing, and you'll become more confident in your math skills!