Lesson 6 iNumbers Solidify Understanding
Solve each system of equations.
Identify the following statements as sometimes true, always true, or never true. If your answer is sometimes true, give an example of when it’s true and an example of when it’s not true. If it’s never true, give a counterexample.
The product of a whole number and a whole number is a whole number.
The product of an integer and an integer is an integer.
The quotient of a whole number divided by a whole number is a whole number.
The product of two rational numbers is a rational number.
The product of two irrational numbers is an irrational number.
The difference of a linear function and a linear function is an integer.
The sum of a linear function and a quadratic function is a quadratic function.
Indicate if the statement is true or false. If it is false, find a counterexample to prove the claim is false. (Recall that a set of number is closed under an operation if it will always produce another number in the same set.)
The set of irrational numbers is closed under addition.
The set of integers is closed under addition and multiplication.
The set of irrational numbers is closed under multiplication.
Find the product of each pair of conjugates.
Find the two complex solutions.