In the following exercise, use the expression $1+\frac{z}{3}+2 w$.

Which part of the expression is a quotient? Describe its parts.

In the following exercise, simplify the given expression.

$$3 z+\frac{3}{4}-2 z$$

In the following exercise, use properties of operations to complete the equivalent expression.

$5(3 x-9)$ and $\underline{\quad}x-\underline{\quad}$

Evaluate the following numerical expression.

$$94-(5 \times 6) \div 6 \times 11$$

In the following exercise, evaluate the given expression.

$$8+6-2 \times 2-3^2$$

In the following exercise, evaluate the expressions when t = 8, w = 1/2, and x = 3.

$$t^2-12 w \div x$$

In the following exercise, simplify the given expression.

4y-y

In the following exercise, write the exponent for the given expression.

$$\left(\frac{2}{3}\right)^8$$

Al's garden is 18 feet long and 30 feet wide. He wants to put fence posts the same distance apart along all sides of the garden. What is the greatest distance apart that Al can place the fence posts?

Peanuts are sold in 8-ounce and 12 -ounce packages. What is the fewest number of ounces you can buy of each package to have equal amounts of each package size?

Critique Reasoning Ron is trying to find the LCM of 4 and 6 . His work is shown at the right. What is Ron's mistake? Explain how to find the correct LCM of 4 and 6. 4: $2 \times 2$ 6: $2 \times 3$ $2 \times 2 \times 2 \times 3=24$, so the LCM of 4 and 6 is 24 .

In the following exercise, write an algebraic expression for each situation.

six times the quantity two x plus three y

Insert grouping symbols so that the expression has the given value. Target value: 23. Expression: $5^2-0.2 \times 8+12 \times \frac{1}{2}$

Josephine's math study group is doing a research project. There are 5 students in her group. In January, each group member surveyed x volunteers and gave a 10-minute presentation. Each volunteer completed a follow-up survey in May. Josephine wrote the expression $5(6 x+25 x+10)$ to represent the total time in minutes that her group spent surveying volunteers and giving presentations.

How can you use properties of operations to write an equivalent expression? Explain your reasoning.