Expressions, Equations, and Functions

Evaluate the following expression and name the property used in each step:

$\mathbf{1}\frac{\mathbf{5}}{\mathbf{6}}\mathbf{\cdot }\mathbf{24}\mathbf{\cdot }\mathbf{3}\frac{\mathbf{1}}{\mathbf{11}}$

 Examples 2 and 3 Evaluate each expression using properties of numbers. Name the property used in each step.

28. $\mathbf{2}\frac{\mathbf{3}}{\mathbf{4}}\mathbf{\cdot }\mathbf{1}\frac{\mathbf{1}}{\mathbf{8}}\mathbf{\cdot }\mathbf{32}$

The sign shows the equipment rented or sold by a scuba diving store.

COOKIES Bobby baked 2 dozen chocolate chip cookies, 3 dozen sugar cookies, and a dozen oatmeal raisin cookies. How many total cookies did he bake?

Evaluate each expression if $\mathit{a}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{,}\mathit{b}\mathbf{=}\mathbf{4}\mathbf{,}$ and $\mathit{c}\mathbf{=}\mathbf{6}$.

31. $\mathbf{4}\mathit{a}\mathbf{+}\mathbf{9}\mathit{b}\mathbf{-}\mathbf{2}\mathit{c}$

Evaluate each expression if $\mathit{a}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{,}\mathit{b}\mathbf{=}\mathbf{4}\mathbf{,}\mathbf{\text{\hspace{0.33em}and }}\mathit{c}\mathbf{=}\mathbf{6}$.

32.$\mathbf{-}\mathbf{10}\mathit{c}\mathbf{+}\mathbf{3}\mathit{a}\mathbf{+}\mathit{a}$ 

Evaluate each expression if $\mathit{a}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{,}\mathit{b}\mathbf{=}\mathbf{4}\mathbf{,}\mathbf{\text{\hspace{0.33em}and }}\mathit{c}\mathbf{=}\mathbf{6}$.

33. $\mathit{a}\mathbf{-}\mathit{b}\mathbf{+}\mathbf{5}\mathit{a}\mathbf{-}\mathbf{2}\mathit{b}$

Evaluate each expression if $\mathit{a}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{,}\mathit{b}\mathbf{=}\mathbf{4}\mathbf{,}\mathbf{\text{\hspace{0.33em}and }}\mathit{c}\mathbf{=}\mathbf{6}$.

34. $\mathbf{8}\mathit{a}\mathbf{+}\mathbf{5}\mathit{b}\mathbf{-}\mathbf{11}\mathit{a}\mathbf{-}\mathbf{7}\mathit{b}$

Evaluate each expression if $\mathit{a}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{,}\mathit{b}\mathbf{=}\mathbf{4}\mathbf{,}\mathbf{\text{\hspace{0.33em}and }}\mathit{c}\mathbf{=}\mathbf{6}$.

35. $\mathbf{3}{\mathit{c}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathit{c}\mathbf{+}\mathbf{2}{\mathit{c}}^{\mathbf{2}}$

Evaluate each expression if $\mathit{a}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{,}\mathit{b}\mathbf{=}\mathbf{4}\mathbf{,}\mathbf{\text{\hspace{0.33em}and }}\mathit{c}\mathbf{=}\mathbf{6}$.

36.  $\mathbf{3}\mathit{a}\mathbf{-}\mathbf{4}{\mathit{a}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathit{a}$

A football team is on the 35-yard line. The quarterback is sacked at the line of scrimmage. The team gains 0 yards, so they are still at the 35-yard line. Which identity or property does this represent? Explain.

Find the value of $\mathit{x}$. Then name the property used.

38. $\mathbf{8}\mathbf{=}\mathbf{8}\mathbf{+}\mathit{x}$

Evaluate the value of $\mathit{x}$ and name the property used in each step:

$\mathbf{10}\mathit{x}\mathbf{=}\mathbf{10}$

Find the value of $\mathit{x}$. Then name the property used.

41. $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\cdot }\mathit{x}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\cdot }\mathbf{7}$

Find the value of $\mathit{x}$. Then name the property used.

42. $\mathit{x}\mathbf{+}\mathbf{0}\mathbf{=}\mathbf{5}$

Evaluate the value of $\mathit{x}$ and name the property used in each step:

$\mathbf{1}\mathbf{\cdot }\mathit{x}\mathbf{=}\mathbf{3}$

Evaluate the value of $\mathit{x}$ and name the property used in each step:

$\mathbf{5}\mathbf{\cdot }\frac{\mathbf{1}}{\mathbf{5}}\mathbf{=}\mathit{x}$

Evaluate the value of $\mathit{x}$ and name the property used in each step:

$\mathbf{2}\mathbf{+}\mathbf{8}\mathbf{=}\mathbf{8}\mathbf{+}\mathit{x}$

Evaluate the value of x and name the property used in each step:

$\mathit{x}\mathbf{+}\frac{\mathbf{3}}{\mathbf{4}}\mathbf{=}\mathbf{3}\mathbf{+}\frac{\mathbf{3}}{\mathbf{4}}$

Evaluate the value of $\mathit{x}$ and name the property used in each step:

$\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\mathit{x}\mathbf{=}\mathbf{1}$

Write an expression to represent the perimeter of the triangle. Then find the perimeter if $\mathit{x}\mathbf{=}\mathbf{2}$ and $\mathit{y}\mathbf{=}\mathbf{7}$.

Sports tickets to a baseball game cost \(25 each plus a \)4.50 handling charge per ticket. If Sharon has a coupon for $10 off and orders 4 tickets, how much will she be charged?

Express the following percent as a fraction or mixed number in the simplest form.

5%

Express the following percent as a fraction or mixed number in the simplest form.

60%

Express the following percent as a fraction or mixed number in the simplest form.

11%

Express the following percent as a fraction or mixed number in the simplest form.

120%

Express the following percent as a fraction or mixed number in the simplest form.

78%

Express the following percent as a fraction or mixed number in the simplest form.

2.5%

Express the following percent as a fraction or mixed number in simplest form.

0.6%

Express the following percent as a fraction or mixed number in the simplest form.

0.4%

Express the following percent as a fraction or mixed number in the simplest form.

1400%

Use the percent proportion to find the following number.

25 is what percent of 125?

Use the percent proportion to find the following number.

16 is what percent of 40

Use the percent proportion to find the following number.

14 is 20% of what number?

Use the percent proportion to find the following number.

50% of what number is 80%?

Use the percent proportion to find the following number.

What is 25% of 18?

Use the percent proportion to find the following number.

Find 10% of 95?

Use the percent proportion to find the following number.

What percent of 48 is 30?

Use the percent proportion to find the following number.

What number is 150% of 32?

Use the percent proportion to find the following number.

5% of what number is 3.5?

Use the percent proportion to find each number.

1 is what percent of 400?

Use the percent proportion to find each number.

Find 0.5% of 250.

Use the percent proportion to find each number.

49 is 200% of what number?

Use the percent proportion to find each number.

15 is what percent of 12?

BASKETBALL Madeline usually makes 85% of her shots in basketball. If she attempts 20, how many will she likely make

A regular octagon measures $\left(3x+5\right)$ units on each side. What is the perimeter if $x=2$?

Write two equations showing the transitive property of equality. Justify your reasoning.

Does the Commutative Property sometimes, always, or never hold for subtraction? Explain your reasoning.

Explain whether 1 can be an additive identity. Give an example to justify your answer.

WHICH ONE DOESN'T BELONG? Identify the sentence that does not belong with the other three. Explain your reasoning.