Question - Understanding Order of Operations in Expressions
Solution:
The equation from the image is:\[ 8 \div 2(2 + 2) = ? \]To solve the equation, follow the order of operations, which is commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).First, solve the expression in the parentheses:\[ 2 + 2 = 4 \]Next, according to the order of operations, you should perform the multiplication before the division when they are consecutive without any parentheses separating them. However, if you interpret the equation as having implicit parentheses, like $$ 8 \div (2(2 + 2)) $$, you would first multiply $$ 2 \times 4 $$ and then divide 8 by the result.Since there's an ambiguity and different interpretations lead to different answers, I'll show you both ways:1. Multiplication first (following strict left-to-right for division and multiplication):\[ 8 \div 2 \times 4 = 4 \times 4 = 16 \]2. Implicit parentheses around the multiplication, indicating that the multiplication is part of the divisor:\[ 8 \div (2 \times 4) = 8 \div 8 = 1 \]Please use the interpretation that aligns with the conventions you are being taught or the one that you intend to use.
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