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Chapter 2: Problem 55

Simplify. \(20 \div(4+6) \cdot 5\)

Short Answer

Expert verified
The simplified expression is 10.

Step by step solution

01

Simplify the expression inside the parentheses

Look at the expression inside the parentheses: (4 + 6). Add these numbers together to get 10.
02

Rewrite the expression

Replace (4 + 6) with 10 in the original expression: 20 division sign 10 multiplication sign 5.
03

Perform the division

Next, divide 20 by 10. This gives you 2.
04

Perform the multiplication

Finally, multiply 2 by 5 to get 10.

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Key Concepts

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

order of operations
Solving arithmetic problems correctly relies on following the right 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). This sequence ensures that everyone arrives at the same final answer.
When simplifying an expression like the one in the exercise, it is essential to begin by handling any calculations inside parentheses. Only afterwards should you proceed with multiplication and division steps.
Following the right order avoids mistakes and keeps the process straightforward.
Always keep PEMDAS in mind for clear and accurate arithmetic calculations.
parentheses in arithmetic
In arithmetic, parentheses are like markers signaling which part of the expression to solve first. They can significantly change an expression's outcome by altering the order of operations.
For the given exercise, the part inside the parentheses is (4 + 6), which simplifies to 10. This step must be done first due to the rules of PEMDAS. Ignoring parentheses or not solving them first could lead to completely different results.
Here鈥檚 a quick recap of the steps:
  • Simplify what's inside the parentheses: (4 + 6) becomes 10.
  • After resolving parentheses, proceed with the remaining operations in the correct order.
Understanding and handling parentheses correctly is crucial for solving complex expressions accurately.
division and multiplication steps
Once parentheses are handled, the next steps are division and multiplication. According to PEMDAS, these operations are performed from left to right.
In the exercise, after simplifying the parentheses, the expression becomes 20 梅 10 脳 5.
First, perform the division:
\[ 20 梅 10 = 2 \]
Then, move on to the multiplication:
\[ 2 脳 5 = 10 \]
Following this order avoids missteps and confusion. Always work from left to right for division and multiplication, ensuring a consistent and correct result.
Breaking down each step keeps the process clear and manageable, leading to the right answer every time.

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