Chi Needs To Simplify The Expression Below.(1.25 Minus 0.4) Divided By 7 + 4 Times 3Which Operation Should
Understanding how to simplify complex mathematical expressions is a fundamental skill in mathematics that applies to various fields, from basic arithmetic to advanced algebra and calculus. When faced with expressions like "(1.25 minus 0.4) divided by 7 plus 4 times 3," it becomes essential to follow a systematic approach to determine the correct operation to perform first and simplify the expression accurately. This article aims to guide you through the process of simplifying such expressions step-by-step, emphasizing the importance of understanding the order of operations.
Understanding the Expression
Before diving into the solution, let's carefully analyze the given expression:
(1.25 minus 0.4) divided by 7 + 4 times 3
At first glance, the expression includes several operations: subtraction, division, addition, and multiplication. To simplify it correctly, we need to understand the order in which these operations should be performed.
Breaking Down the Expression
The expression can be written as:
(1.25 - 0.4) ÷ 7 + 4 × 3
which involves the following components:
- Subtraction: 1.25 - 0.4
- Division: The result of the subtraction divided by 7
- Multiplication: 4 times 3
- Addition: Combining the division result and the multiplication result
Order of Operations (PEMDAS/BODMAS)
The key to simplifying any complex expression is understanding the order of operations, often summarized by the acronym PEMDAS or BODMAS:
- P/B: Parentheses/Brackets
- E/O: Exponents/Orders (powers and roots)
- MD: Multiplication and Division (from left to right)
- AS: Addition and Subtraction (from left to right)
Applying this rule ensures that everyone simplifies expressions consistently and correctly.
Prioritizing Operations in Our Expression
In our specific expression:
(1.25 - 0.4) ÷ 7 + 4 × 3
the steps are:
- Simplify inside parentheses: 1.25 - 0.4
- Perform the division: (result from step 1) ÷ 7
- Calculate the multiplication: 4 × 3
- Add the results from steps 2 and 3
Let's analyze each step in detail.
Step-by-Step Simplification Process
Step 1: Simplify Inside Parentheses
Calculate 1.25 - 0.4:
- 1.25 - 0.4 = 0.85
Step 2: Perform Division
Divide the result from step 1 by 7:
- 0.85 ÷ 7 ≈ 0.1214 (rounded to four decimal places)
Step 3: Perform Multiplication
Calculate 4 × 3:
- 4 × 3 = 12
Step 4: Final Addition
Add the results from steps 2 and 3:
- 0.1214 + 12 ≈ 12.1214
Therefore, the simplified value of the entire expression is approximately 12.1214.
Which Operation Should Chi Perform First?
Based on the order of operations, Chi should perform the following:
- Parentheses first: Simplify 1.25 - 0.4
- Division next: Divide the result by 7
- Multiplication: Calculate 4 × 3
- Addition last: Add the division result and the multiplication result
This order ensures an accurate and systematic simplification process.
Common Mistakes to Avoid
While simplifying expressions, it's easy to make mistakes if the order of operations isn't followed carefully. Here are some common errors and tips to avoid them:
1. Ignoring Parentheses
- Always evaluate expressions inside parentheses or brackets first.
- Example mistake: Adding 7 + 4 before dividing or subtracting.
2. Performing Multiplication and Division in the Wrong Order
- Remember that multiplication and division are of equal priority; perform them from left to right.
- Example mistake: Dividing before subtracting the parentheses content.
3. Misinterpreting the Expression
- Ensure the expression is correctly parsed: parentheses, multiplication, division, addition.
- Break complex expressions into smaller parts for clarity.
Practice Problems to Reinforce Learning
To solidify understanding, try simplifying the following expressions:
- (2 + 3) × 4 - 5
- 10 ÷ (2 + 3)
- (8 - 3) × 2 + 4
- 6 + 4 × (2 - 1)
- (3 + 5) ÷ 2 + 7
Answers:
- (2 + 3) × 4 - 5 = 5 × 4 - 5 = 20 - 5 = 15
- 10 ÷ (2 + 3) = 10 ÷ 5 = 2
- (8 - 3) × 2 + 4 = 5 × 2 + 4 = 10 + 4 = 14
- 6 + 4 × (2 - 1) = 6 + 4 × 1 = 6 + 4 = 10
- (3 + 5) ÷ 2 + 7 = 8 ÷ 2 + 7 = 4 + 7 = 11
Conclusion: The Key to Simplifying Expressions
Chi's task of simplifying the expression emphasizes the importance of following the order of operations meticulously. Always start with parentheses, then move to exponents (if any), followed by multiplication and division from left to right, and finally addition and subtraction from left to right. Mastering this process not only leads to correct solutions but also builds a strong foundation for tackling more complex mathematical problems. Remember, systematic approach and careful attention to the order of operations are the keys to success in mathematics.
