Solving the Mathematical Expression: 9 - 9 × 99
Solving the Mathematical Expression: 9 - 9 × 99
When looking at mathematical expressions, it is essential to understand the proper order of operations to arrive at the correct answer. The expression in question is 9 - 9 × 99, which can be solved using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), or BODMAS (Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).
Following the Order of Operations
The first step in solving the expression 9 - 9 × 99 is to perform the multiplication. According to PEMDAS/BODMAS, multiplication is given priority over subtraction.
Multiplication
Step 1: Calculate 9 × 99.
9 × 99 891
Now, we substitute back into the expression, resulting in:
9 - 891
Step 2: Perform the subtraction from left to right.
9 - 891 -882
The final answer is -882. However, it appears the original expression had a typo, and it might have been intended to be 9 - 9 × 9 (99 without the second 9), which leads to a different result. Let's solve 9 - 9 × 9 following the same order of operations.
Correct Expression: 9 - 9 × 9
Step 1: Calculate 9 × 9.
9 × 9 81
Step 2: Substitute back and perform the subtraction.
9 - 81 -72
Step 3: Finally, divide by 9 (if applicable, but the final operation is subtraction).
-72 / 9 -8
So, the correct answer to the expression 9 - 9 × 9 is -8.
However, based on the original expression 9 - 9 × 99, the correct answer is -882. It seems there is a misunderstanding or a typo in the initial problem statement.
Alternative Methods
Several methods have been suggested for solving the expression:
DMAS Method
Using the DMAS (Division, Multiplication, Addition, Subtraction) rule:
Step 1: Perform the multiplication first.
9 - (9 × 99) 9 - 891
Step 2: Perform the subtraction.
9 - 891 -882
Thus, the final answer is -882.
VBODMAS Method
Using the VBODMAS (V for vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction) rule:
Step 1: Perform the multiplication.
9 - (9 × 99) 9 - 999
Step 2: Perform the subtraction from left to right.
9 - 999 -891
Therefore, the final answer is -891.
Common Mistakes
It is important to note that many people might mistakenly solve the expression 9 - 9 × 99 by performing the subtraction first, which is incorrect. The correct order of operations must be followed to get the accurate answer.
Learning from Mistakes
Understanding the importance of following the order of operations is crucial, even for basic arithmetic expressions. Math is a fundamental skill, and mastering it can significantly enhance problem-solving abilities in various fields.
Conclusion
The expression 9 - 9 × 99, when solved correctly, results in -882. However, if the intention was 9 - 9 × 9, the correct answer would be -8. This example reinforces the importance of carefully following the order of operations to solve mathematical expressions accurately.