options: Use complex numbers in polynomial identities and equations.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Perform operations on matrices and use matrices in applications.

Perform operations on vectors.

Extend the properties of exponents to rational exponents.

Perform arithmetic operations with complex numbers.

Reason quantitatively and use units to solve problems.

Apply and extend previous understandings of numbers to the system of rational numbers.

Represent and model with vector quantities.

Represent complex numbers and their operations on the complex plane.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Use properties of rational and irrational numbers.

Compute fluently with multi-digit numbers and find common factors and multiples.
problem_activity: Task
Explain why the sum and product of two rational numbers is always a rational number.
Kaylee says
I know that $\pi$ is an irrational number so its decimal never repeats. I also know that $\frac{1}{7}$ is a rational number so its decimal repeats. But I don't know how to add or multiply these decimals so I am not sure if $\pi + \frac{1}{7}$ and $ \pi \times \frac{1}{7}$ are rational or irrational.
Using part (a), help Kaylee decide whether or not $\pi + \frac{1}{7}$ and $\pi \times \frac{1}{7}$ are rational or irrational.


correct_option_index: 12