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Why doesn't the distributive property always work for division?
The distributive property works is defined for multiplication and addition: a (b + c) = ab + ac also: (a + b)c = ac + bc For a division, it works if you can convert it into a multiplication, in a form similar to the above. For example: (10 + 2) / 2 can be converted into a multiplication; in this case, dividing by 2 is equivalent to multiplying by 1/2: (10 + 2) (1/2) = (10 x 1/2) + (2 x 1/2) If the sum is in the divisor, for example: 15 / (1 + 2) then there is no way you can convert it into an equivalent multiplication, which conforms to the forms used for the distributive property.
How are quotients and products similar and different?
A quotient is the answer of a division question and the product is the answer of a multiplication question but they are the same because they are both an answer to a math problem.
The transitive property holds for similar figures?
The transitive property states that if A is equal to B, and B is equal to C, then A is equal to C. In the context of similar figures, this property holds true. If two figures are similar, and one figure is congruent to a third figure, then the second figure is also congruent to the third figure.
How do you simplify an algebraic term?
That depends a lot on the term. Some of course can't be simplified - each expression has a simplest possible equivalent, no matter how you define "simple". Sometimes you can add similar terms; sometimes you can use laws of powers to simplify terms; sometimes you can use the distributive property; etc. You just have to go through an algebra book, and do lots of exercises, to get the hang of what you can do.
How is the Transitive Property of Parallel Lines similar to the Transitive Property of Congruence?
If A ~ B and B ~ C then A ~ C. The above statement is true is you substitute "is parallel to" for ~ or if you substitute "is congruent to" for ~.
