/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 Simplify. $$-10^{2} \div 2 \cd... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 65

Simplify. $$-10^{2} \div 2 \cdot 5-3$$

Short Answer

Expert verified
Simplified result is 247.

Step by step solution

01

Address the Exponent

First, evaluate the exponent in the expression. Calculate \(-10^{2}\). This means \(-10\) raised to the power of 2, which equals \(-10 \times -10 = 100\). So, the expression becomes: \(100 \div 2 \cdot 5 - 3\)
02

Division Operation

Next, perform the division operation. Calculate \(100 \div 2\). This gives \(50\). Now the expression is: \(50 \cdot 5 - 3\)
03

Multiplication Operation

Then, perform the multiplication operation. Calculate \(50 \cdot 5\). This results in \(250\). Now the expression is: \(250 - 3\)
04

Subtraction Operation

Finally, perform the subtraction operation. Calculate \(250 - 3\). This gives \(247\).

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Key Concepts

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

Order of Operations
When simplifying algebraic expressions, it is crucial to follow the order of operations. This set of rules ensures that everyone solves the expression the same way and gets the same result. The common acronym to remember is PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In the given problem \(-10^{2} \ \div 2 \cdot 5-3\), start with exponents, move to division and multiplication, then end with addition and subtraction. This process ensures accurate results.
Exponents
Exponents represent a number raised to the power. For example, \(x^n\) means x is multiplied by itself n times. In our exercise, \(-10^{2}\) means \(-10\) is multiplied by itself, not simply that the exponent applies to the 10 alone. So:\-10^{2} = (-10) \times (-10) = 100\. Exponents must be handled before any multiplication, division, addition, or subtraction to ensure accuracy.
Division and Multiplication
After dealing with parentheses and exponents, proceed with division and multiplication. These operations are of equal priority and should be completed from left to right. In the example, after calculating the exponent, we have \(100 \div 2 \cdot 5-3\) following the left-to-right rule:\100 \div 2 = 50\ and then \50 \cdot 5 = 250\. Completing these steps correctly will help avoid errors in the final result.
Addition and Subtraction
Lastly, perform any addition and subtraction from left to right. After completing all previous operations in our expression \(250 - 3\), we are left with a simple subtraction. The result:\250 - 3 = 247\ completes the simplification. Each arithmetic operation must be handled in its specific order to ensure accurate and consistent outcomes.

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