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
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Your response:
Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Reason quantitatively and use units to solve problems.

Use complex numbers in polynomial identities and equations.

Perform arithmetic operations with complex numbers.

Perform operations on matrices and use matrices in applications.

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

Represent complex numbers and their operations on the complex plane.

Use properties of rational and irrational numbers.

Extend the properties of exponents to rational exponents.

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

Represent and model with vector quantities.

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

Perform operations on vectors.

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

Compute fluently with multi-digit numbers and find common factors and multiples.
problem_activity: Problem 1
Write each rational number in the form
$${a\over{b}}$$
, where
$$a$$
and
$$b$$
are integers, and
$$b\neq0$$
.
a.
$${0.3333}$$
b.
$${-5.05}$$
c.
$${\sqrt{64}}$$
e.
$${\sqrt{4\over25}}$$
f.
$${\sqrt{1.21}}$$
Problem 2
A student wrote two repeating decimals as fractions using the strategy shown below.
| Given the decimal                       $$0.\overline{12}$$                       Let                       $$x=0.\overline{12}$$                       Then                         $$100x=12.\overline{12}$$              |https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2a.PNG|  |https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2a.PNG| image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2a.PNG | Given the decimal                       $$0.\overline{123}$$                       Let                       $$x=0.\overline{123}$$                       Then                       $$1000x=123.\overline{123}$$             |https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2b.PNG|  |https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2b.PNG| image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2019/02/06/math8_u7_l5_ap2b.PNG |
|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
a.   Describe the student’s strategy in your own words.
b.   Use the same strategy to write the two decimals below as fractions.
$${0.\overline{54}}$$
$${0.1\overline{23}}$$
Problem 3
What is the sum of
$${0.1}$$
and
$${0.\overline3}$$
written as a fraction?


correct_option_index: 12