options: Perform arithmetic operations with complex numbers.

Use properties of rational and irrational numbers.

Use complex numbers in polynomial identities and equations.

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

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

Extend the properties of exponents to rational exponents.

Represent and model with vector quantities.

Represent complex numbers and their operations on the complex plane.

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

Perform operations on vectors.

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.

Reason quantitatively and use units to solve problems.

Apply and extend previous understandings of numbers to the system of rational numbers.
problem_activity: Problem 1
Evaluate the following numerical expressions.
a.
$${-2(5+(3)(-2)+4)}$$
b.
$${-2((5+3)(-2+4))}$$
c.
$${-2(5+3(-2+4))}$$
d.   Can the parentheses in any of these expressions be removed without changing the value of the expression?
Problem 2
An expression is shown below with three expressions that are
not
equivalent to it. Explain the error(s) that were made in writing each expression.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
a.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{3(-4)}{2(3)^2}$$
b.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{6-3(-4)}{(6)^2}$$
c.
$$\frac{6-3(4-8)}{2(1+2)^2}$$
$$\neq \frac{6-12}{(2+4)^2}$$
d.   Evaluate the expression.
Problem 3
Evaluate:
$${\frac{1}{2}(-3-1)^2-\left ( 10 \div \frac{5}{6} \right )}$$


correct_option_index: 11