Final answer:
The distributive property in algebra allows multiplication or division to be distributed across terms within brackets, ensuring each term is affected equally. It is essential for maintaining equality in an expression when simplifying or evaluating.
Step-by-step explanation:
The distributive property is used in algebra to simplify and evaluate expressions where multiplication is distributed over terms in summation. To apply the distributive property, multiply or divide every term inside the brackets by the number outside the brackets. For example, if you have an expression like 3(x + 4), you would apply the distributive property by multiplying both the x and 4 by 3, resulting in 3x + 12. This concept ensures the equation remains an equality by performing the same operation on each term.
When simplifying expressions, always eliminate terms wherever possible and check if your final answer is reasonable. The distributive property also applies when working with complex fractions, ensuring the numerator and denominator are treated equally.