The distributive property and the order of operations are two important concepts in mathematics that are used in different situations.
The distributive property states that when you have a number multiplied by a sum (or difference), you can distribute the multiplication across the addition (or subtraction). For example, in the expression a(b + c), you can use the distributive property to rewrite it as ab + ac. This property is particularly useful when simplifying expressions or solving equations where multiplication is involved.
On the other hand, the order of operations is a set of rules that dictates the sequence in which different operations should be performed to accurately evaluate an expression. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. You use the order of operations whenever you simplify or evaluate complex expressions that involve multiple operations.
In summary, use the distributive property when you need to simplify an expression by distributing a multiplication over addition or subtraction. Use the order of operations when evaluating an expression that contains a mix of different operations to ensure you perform them in the correct sequence.