अभिव्यक्तियों का सरलीकरण और क्रम

Simplifying Expressions using Order of Operations

• The expression involves various operations: addition, subtraction, division, and brackets. Order of operations (PEMDAS/BODMAS) dictates the sequence in which these operations are performed.
• PEMDAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right) is a crucial rule in evaluating expressions.

Evaluating the Expression

• The expression is 25 - 1 / 2 { 5 + 4 - ( 3 + 2 - 1 + 3 )}
• First step: Parentheses/Brackets. Focus on the innermost set of brackets first:
  • 3 + 2 - 1 + 3 = 7
• Second step: Simplify the expression within the next set of brackets:
  • 5 + 4 - 7 = 2
• Third step: The expression now is 25 - 1 / 2 {2}
• Fourth step: Brackets again:
  • 25 - 1/4
• Fifth step: Division:
  • 1/2 = 0.5; Now we have 25 - 0.5 * 2
  • 0.5 * 2 = 1
• Sixth step: Subtraction:
  • 25 - 1 = 24

Integer Arithmetic

• The expression uses integers (positive and negative whole numbers).
• Operations involve integer addition, subtraction, multiplication, and division. Following the order of operations (PEMDAS) is critical for accuracy.

Bracket Notation

• Brackets in mathematics (parentheses, curly braces, and square brackets) define an operation or grouping of values
• Correctly using bracket notation is essential for avoiding mistakes.
• Innermost brackets are evaluated first.

Evaluating Expressions

• Evaluating an expression means finding its numerical value. This requires following the rules of precedence, particularly the order of operations (PEMDAS/BODMAS).
• Simplification procedures are necessary steps in reaching the numerical answer.

Order of Operations

• Order of operations is the sequence in which operations in a mathematical expression are to be performed.
• PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), provide a universal standard.
• Incorrect order of operations will lead to an incorrect solution.

Final Answer

• 25 - 1/2{5 + 4 - (3 + 2 - 1 + 3)} = 24

इस क्विज़ में अभिव्यक्तियों को सरलीकृत करने में सहायता मिलेगी, जहाँ आप क्रम (PEMDAS/BODMAS) के नियमों का पालन करते हुए विभिन्न गणितीय संचालन में सुधार करेंगे। इसमें जोड़, घटाव, विभाजन और ब्रैकेट्स का उपयोग कर अभिव्यक्तियों का विश्लेषण किया जाएगा।