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

Perform operations on matrices and use matrices in applications.

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

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

Use complex numbers in polynomial identities and equations.

Compute fluently with multi-digit numbers and find common factors and multiples.

Perform operations on vectors.

Use properties of rational and irrational numbers.

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

Represent and model with vector quantities.

Extend the properties of exponents to rational exponents.

Reason quantitatively and use units to solve problems.

Perform arithmetic operations with complex numbers.

Represent complex numbers and their operations on the complex plane.
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: 7