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🍬honors algebra ii review

key term - PEMDAS

Citation:

Definition

PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It serves as a guideline for the order of operations in mathematics, ensuring that calculations are performed in a consistent and correct sequence. Understanding PEMDAS is crucial when working with real numbers and algebraic expressions, as it dictates how to approach complex equations without ambiguity.

5 Must Know Facts For Your Next Test

  1. PEMDAS is sometimes remembered using the phrase 'Please Excuse My Dear Aunt Sally' to help recall the order of operations.
  2. When evaluating expressions with multiple operations, always start with anything inside parentheses first before proceeding to exponents.
  3. Multiplication and division are treated equally; you perform them from left to right as they appear in the expression.
  4. Addition and subtraction are also treated equally and are executed last, again from left to right.
  5. Using PEMDAS correctly prevents misinterpretation of mathematical expressions, leading to accurate solutions.

Review Questions

  • How does applying PEMDAS affect the evaluation of an algebraic expression involving multiple operations?
    • Applying PEMDAS ensures that an algebraic expression is evaluated correctly by following a specific order of operations. For example, in the expression $$3 + 6 \times (5 + 4) \div 3 - 7$$, you first solve the parentheses $$5 + 4$$, then handle multiplication and division from left to right before finally performing addition and subtraction. This approach prevents confusion and ensures that the final answer reflects the intended calculations.
  • In what ways can misunderstanding PEMDAS lead to errors in calculations involving real numbers?
    • Misunderstanding PEMDAS can lead to significant errors in calculations involving real numbers by causing individuals to perform operations out of order. For instance, if someone calculates $$8 + 2 \times 5$$ by adding first instead of multiplying, they would arrive at an incorrect result of 50 instead of the correct answer, which is 18. Recognizing the importance of following the PEMDAS guideline can help avoid these common pitfalls and promote accuracy.
  • Evaluate the expression $$2 + 3 \times (8 - 2)^{2} \div 4$$ using PEMDAS, and explain how each step adheres to this order of operations.
    • To evaluate $$2 + 3 \times (8 - 2)^{2} \div 4$$ using PEMDAS, start with parentheses: $$8 - 2 = 6$$. Next, handle the exponent: $$6^{2} = 36$$. Now your expression looks like $$2 + 3 \times 36 \div 4$$. Following multiplication and division from left to right, calculate $$3 \times 36 = 108$$ and then divide by 4: $$108 \div 4 = 27$$. Finally, add: $$2 + 27 = 29$$. Each step demonstrates adherence to the PEMDAS order of operations.