Evaluate.

$\dfrac{a}{3b}$ for $a = 18$ and $b = 3$

Find the area $(A)$ of a basketball court with length $(l)$ of $26\ \text{m}$ and width $(w)$ of $1400\ \text{cm}$ using the formula $A = lw$.

Solve for the given replacement set.

$$x^2 + x = 0\ \ \ \{0, 100, 1000\}$$

Evaluate.

$12 - x$ for $x = 5$

Calculate.

$$(7 + 2)^2$$

Use the distributive property to write an equivalent expression.

$$4(1 + y)$$

Write an equivalent expression using a commutative property.

$$ab + c$$

$\textbf{\textcolor{#4257b2}{Mathematical Reasoning}} \hspace{15pt}$ A student factored $ax + ay + bx + by$ as $a(x + y) + b(x + y)$. Another student factored the same expression as $x(a + b) + y(a + b)$. Are both answers correct, or is one of them incorrect? Justify your answer.

Evaluate.

$(3a^3)$ for $a = 5$

Factor.

$$8 + 16x + 40y$$

$\textbf{\textcolor{#4257b2}{Critical Thinking}} \hspace{15pt}$ You know that $a(b + c) = ab + ac$ for any numbers $a, b,$ and $c$. Use this fact and the properties introduced earlier to write a paragraph explaining why $(b + c)a = ba + ca$ is also true for any numbers $a, b,$ and $c$.

Factor.

$$20a + 30b$$

Simplify.

$$\dfrac{14n}{28ny}$$

Simplify.

$$\dfrac{6mn}{11mt}$$