This example clarifies the purpose of order of operations: to have ONE way to interpret a mathematical statement.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/pre-algebra/order-of-operations/order_of_operations/e/order_of_oper...
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https://www.khanacademy.org/math/pre-algebra/order-of-operations/order_of_operations/v/order-of-oper...
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https://www.khanacademy.org/math/pre-algebra/order-of-operations/rational-irrational-numbers/v/appro...
Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!
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