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Chapter 6: Problem 44

Evaluate the expression. $$35+40 \div 2$$

Short Answer

Expert verified
The result of evaluating the given expression is 55.

Step by step solution

01

Perform Division

The division operation (40 梅 2) should be carried out first, yielding a result of 20.
02

Perform Addition

Next, the addition operation (35 + 20) is performed yielding a result of 55.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Arithmetic Operations
Arithmetic operations are fundamental tasks like addition, subtraction, multiplication, and division. Each operation follows specific rules and orders. When there's more than one operation in an expression, we use the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • Order is crucial: The order ensures consistent and accurate results when solving mathematical problems.
  • Role in combined operations: Recognizing and applying the correct order is the key to solving expressions like the one given.
  • Application in everyday calculations: From calculating costs to planning budgets, arithmetic operations form the backbone of daily computations.
In our exercise, the expression includes both division and addition. Following the order of operations lets us solve it step-by-step correctly.
Division
Division is like undoing multiplication. It answers the question, 'How many times does one number fit into another?' When dividing, be sure to check your work, as mistakes can lead to wrong results downstream in your calculations.
Performing division before addition is key in expressions with multiple operations. This is because the rules of arithmetic tell us to divide before we add.
  • Understanding our exercise: In 40 梅 2, we find how many 2s fit into 40. The answer is 20.
  • Importance of accuracy: Ensuring that division is done correctly affects the subsequent operations, like addition in this case.
So in any expression that combines division with other operations, always tackle division first to maintain accuracy.
Addition
Addition is the arithmetic process where we combine two or more numbers to find their total. It's addition that brings a collection of numbers into a single whole. After division, our focus shifts back to this simple but vital operation.
In our expression, after performing division, we are left with 35 + 20. Addition here means we take the result of the division and add it to the other number.
  • Simple yet essential: Addition is often the final step in evaluating expressions and ensures that we complete the calculation.
  • Importance in our exercise: By adding the numbers correctly, we find the total as 55, giving us the final answer.
  • Versatility: Beyond the realm of abstract numbers, addition helps in areas like measuring distances or combining scores.
In every numerical problem, especially after handling operations like division, addition is the final stitch that ties it all together into a coherent solution.

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