Solving 8×98 with BODMAS: A Comprehensive Guide
Mathematics is a language that requires clarity and precision, and one of the most important tools for ensuring this is the BODMAS rule, which defines the order of operations for solving mathematical expressions. This rule is crucial for solving problems like 8×98 accurately and consistently. In this article, we will explore the BODMAS rule, break down the steps to solve 8×98, and provide additional examples to help you master this essential concept.
What is BODMAS?
The BODMAS rule is an acronym that stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It is a sequence of operations that dictates the order in which mathematical expressions should be solved to ensure the correct result.
Breaking Down BODMAS
Let's take a closer look at each component of the BODMAS rule:
B - Brackets: Solve expressions within brackets first, starting with parentheses ( ) followed by square brackets [ ] and then curly brackets { }. This step is critical for addressing any parentheses, exponentiation, or nested expressions within the bracket system. O - Orders: Orders refer to exponents and roots. After solving the expressions within brackets, you handle any exponents or roots next. For example, in the expression 43, you calculate the exponent before any other operations. D - Division: Division is the next operation to be performed, but it must be done in the order from left to right. M - Multiplication: Multiplication, similar to division, is performed from left to right. A - Addition: Addition follows division and multiplication, and it is also performed from left to right. S - Subtraction: Finally, subtraction is performed last, from left to right.Solving 8×98 Using BODMAS
Let's apply the BODMAS rule to the specific problem of solving 8×98. The expression is quite straightforward, but it's still a good exercise to walk through the steps:
Step-by-Step Solution
Check for Brackets: There are no brackets in this expression. Therefore, we skip this step and move to the next. Check for Orders: There are no exponents or roots in this expression. We skip to the next step. Division: There is no division in this expression. We skip this step. Multiplication: We need to perform the multiplication first. So, 8×98. Let's break it down further for clarity:8×98 784Addition: There is no addition in this expression. We skip this step. Subtraction: There is no subtraction in this expression. We skip this step.
Thus, the correct answer to the expression 8×98 is 784.
Common Misconcept and Clarifications
There seems to be a confusion about the problem 8×98, leading to some incorrect results. Let's address a common misconception:
Some sources incorrectly provide that 8×98 equals 80. However, based on the BODMAS rule, this is incorrect. The multiplication should be performed first, resulting in:
8×98 784
This result is derived by following the correct order of operations. Let's break down the steps again:
No brackets: 8×98 No orders: 8×98 No division: 8×98 Multiplication: 8×98 784 No addition: 784 No subtraction: 784Thus, 8×98 equals 784, not 80.
Additional Examples
To further solidify your understanding, let's look at a few more examples of expressions that can be solved using the BODMAS rule:
Example 1: 3 6 × (5 4) ÷ 3 - 7
Brackets: (5 4) 9 Expression now becomes: 3 6 × 9 ÷ 3 - 7 Orders: No exponents or roots. Division: 9 ÷ 3 3 Expression now becomes: 3 6 × 3 - 7 Multiplication: 6 × 3 18 Expression now becomes: 3 18 - 7 Addition: 3 18 21 Expression now becomes: 21 - 7 Subtraction: 21 - 7 14The result of 3 6 × (5 4) ÷ 3 - 7 is 14.
Example 2: 20 ÷ 4 3 × 5 - 2
Brackets: No brackets. Orders: No exponents or roots. Division: 20 ÷ 4 5 Expression now becomes: 5 3 × 5 - 2 Multiplication: 3 × 5 15 Expression now becomes: 5 15 - 2 Addition: 5 15 20 Expression now becomes: 20 - 2 Subtraction: 20 - 2 18The result of 20 ÷ 4 3 × 5 - 2 is 18.
By understanding and applying the BODMAS rule, you can accurately solve complex mathematical expressions and avoid common errors.
Conclusion
Mastering the BODMAS rule is crucial for solving a wide range of mathematical problems. Whether it's simple multiplication like 8×98 or complex expressions with multiple operations, following the BODMAS sequence ensures the correct result. Remember to always start with brackets, then handle orders, followed by division and multiplication (from left to right), and finally addition and subtraction (from left to right).
Apply this rule consistently in your calculations, and you will see a marked improvement in your ability to solve mathematical problems.