Understanding and Solving the Mathematical Expression 7-3 5-2
The expression 7 -3 5 -2 can be confusing at first glance. However, by following the correct order of operations, the solution becomes clear. In this article, we'll explore the various solutions and explanations provided and break down the mathematical processes involved.
Using the Order of Operations
To solve the expression, we must adhere to the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). In this case, the expression does not contain any parentheses or exponents, so we proceed with subtraction from left to right.
Solution 1: Correct Application of Subtraction
1. Start with the original expression: 7 - 3 5 - 2.
2. Calculate the multiplication first:
5 times -2 -10.
3. Substitute this back into the expression:
7 - 3 - 10.
4. First, calculate 7 - 3:
7 - 3 4.
5. Then, add -10
4 - 10 -6.
So, the final answer is -6.
Solution 2: Simplified Form
Another way to approach this is by simplifying the expression. Start with the simplification:
7 - 3 - 5 - 2
Simplify step by step:
7 - 3 - 5 - 2 7 - 5 - 2
7 - 5 - 2 2 - 2
2 - 2 0
Therefore, the correct solution is 0.
Understanding Negatives and Subtraction
It is important to note that the solution depends on the correct application of negative numbers and subtraction rules. For example:
7 - 3 4, is clear. However, the next step is to understand that subtracting a negative number is the same as adding the positive counterpart. For instance:
5 - 2 3.
Then, 4 - 10 -6.
Common Mistakes to Avoid
Here are some common mistakes that one might make when solving this expression:
Forgetting to follow the correct order of operations. Misinterpreting the subtraction of a negative number.Always double-check the order of operations and the handling of negative numbers to ensure accurate results.
Conclusion
In conclusion, while the expression 7-3 5-2 can be challenging due to its ambiguous nature, by applying the correct order of operations and understanding the handling of negative numbers, the solution becomes clear. The final correct answer is -6.