is x - y rational or irrational
The expression x - y can be either rational or irrational, depending on the values of x and y.
Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.
is x - y rational or irrational
If x and y are both non-zero rational numbers, then their difference, x - y, will also be a rational number.
So, x - y is rational.
Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.
is 3z rational or irrational
Since z is an irrational number, any multiple of z (such as 3z) will also be irrational. Therefore, 3z is an irrational number.
Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.
is -2x rational or irrational
If x is a non-zero rational number, then (-2)x is also a rational number. Multiplying a rational number by -2 does not change its rationality, as the result is still expressible as a quotient of two integers. Therefore, -2x is rational.
Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.
is y + z rational or irrational