standard_description: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
problem_activity: Task
In each of the following problems, a number is given. If possible, determine whether the given number is rational or irrational. In some cases, it may be impossible to determine whether the given number is rational or irrational. Justify your answers.
$ 4 + \sqrt{7} $
$ \displaystyle \frac{\sqrt{45}}{\sqrt{5}} $
$ \displaystyle \frac{6}{\pi} $
$ \sqrt{2} + \sqrt{3} $
$ \displaystyle \frac{2 + \sqrt{7}}{2a + \sqrt{7a^2}}$, where $a$ is a positive integer
$ x + y$, where $x$ and $y$ are irrational numbers


aligns: no