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Chapter 1: Problem 56

Simplify. $$ 524 \div 32 \div 512 $$

Short Answer

Expert verified
The simplified result is approximately 0.03193359.

Step by step solution

01

Simplify the Expression from Left to Right

Start by solving the first division in the expression: \(524 \div 32\). Divide 524 by 32 to get 16.375. Thus the expression becomes \(16.375 \div 512\).
02

Perform the Next Division

Now, divide the result from the first step (16.375) by 512. Performing this division gives approximately 0.03193359.

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Key Concepts

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

Simplifying Expressions
When faced with a math problem involving division, the goal is to simplify the expression as much as possible. Simplifying an expression means breaking it down to its most basic form. This involves handling the mathematical operations step by step until we arrive at the simplest version of the original expression. For division, simplification involves performing the division operations in sequence. A common approach is:
  • Start the division with the numbers that appear first from the left.
  • Progress through any remaining operations after finding the initial results.
In the case of this exercise, the expression is simplified by taking two division operations: first, dividing 524 by 32, and then using that result to divide by 512. By simplifying in steps, we avoid any confusion and ensure accuracy.
Order of Operations
In mathematics, the order of operations is crucial to arriving at the correct answer. For division, it's important to follow this order strictly. The order of operations is a set of rules that defines the correct sequence to apply different operations within an expression. This is sometimes remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In this particular exercise:
  • You follow the order by doing each division from left to right as they appear in the expression.
  • This ensures that we are not skipping over any numbers or reversing the intended logic of the problem.
By maintaining consistency in the order, you achieve the correct simplified form of the expression.
Step-by-Step Solution
A step-by-step solution can greatly enhance understanding by breaking down the problem into smaller, manageable parts. Let's walk through the division of this expression. First, divide the number 524 by 32. When you do this, you'll get 16.375. The importance of this step is that it sets the stage for the next division. Next, use the result from the first division step. Take 16.375 and divide it by 512. This second division gives you approximately 0.03193359. By processing the solution in steps:
  • Complex calculations become easier to manage.
  • You reduce the margin for error since each step's outcome guides the next.
Remember, breaking down each operation in a methodical way is key to simplifying complex expressions successfully.

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