few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Your response:
Thought: This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001097

7
options: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
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


correct_option_index: 0