First you add what is inside the parentheses. 

$\displaystyle 5+3=8$.

Then, we multiply, 

$\displaystyle 8*2$.

This leaves us with our answer of 16.

To solve, we round $1.03 to $1.00 and round 386 pencils to 400.

Then we would multiply to find the answer, so $\displaystyle 1*400$ would give us the best estimate.

To solve the expression, you must first solve inside the parentheses, so 

$\displaystyle 8-6=2$.

Then we divide 2 by 2 and are left with our answer, 1.

Including Caitlin, there are 5 total people receiving tickets.

If she is going to divide them among her friends, then we would use division,

$\displaystyle \frac{\text{Number of Tickets}}{\text{Number of People}}=\frac{x}{5}$

First we add and are left with 

$\displaystyle \small 6x-x=15$.

Then we subtract and are left with 

$\displaystyle \small 5x=15$.

Finally, in order to get the $\displaystyle \small x$ alone, we divide each side by 5 and are left with 

$\displaystyle \small x=3$.

Following the order of operations, we must do the work inside the parentheses first, so we are left with 

$\displaystyle \small 1+3+6*2=x$.

Then we must multiply and are left with 

$\displaystyle \small 1+3+12=x$.

Finally 

$\displaystyle \small 4+12=x$.

So 

$\displaystyle \small x=16$.

From the question, we know that $\displaystyle 5$ plus a number equals $\displaystyle \frac{3}{5}$ of $\displaystyle 25$. In order to find out what $\displaystyle \frac{3}{5}$ of $\displaystyle 25$ is, multiply $\displaystyle \frac{3}{5}$ by $\displaystyle \frac{25}{1}$.  

$\displaystyle \frac{3}{5}\times\frac{25}{1}=\frac{75}{5}$, or $\displaystyle 15$.

The number we are looking for needs to be five less than $\displaystyle 15$, or $\displaystyle 10$.

You can also solve this algebraically by setting up this equation and solving:

$\displaystyle 5+x=\frac{3}{5}\times25$

$\displaystyle 5+x=15$ 

Subtract $\displaystyle 5$ from both sides of the equation.         

$\displaystyle x=10$

To solve an equation, first combine like terms. Move the $\displaystyle -6$ over to the other side of the equation by adding $\displaystyle +6$:

$\displaystyle 14x - 6=64$

         $\displaystyle +6=+6$

        $\displaystyle 14x=70$

Next, remove the $\displaystyle 14$ from the variable by dividing by $\displaystyle 14$.

$\displaystyle \frac{14x}{14}=\frac{70}{14}\rightarrow x=5$

The answer is $\displaystyle 5$.

Ratios can be written in the following format:

$\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has $\displaystyle 9$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\displaystyle \frac{9\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{9\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$\displaystyle 9\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

$\displaystyle 3T=117$

Divide both sides of the equation by $\displaystyle 3$.

$\displaystyle \frac{3T}{3}=\frac{117}{3}$

Solve.

$\displaystyle T=39$

The farmer can get $\displaystyle 39\ \text{turnips}$.

Ratios can be written in the following format:

$\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has $\displaystyle 27$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\displaystyle \frac{27\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{27\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$\displaystyle 27\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

$\displaystyle 3T=351$

Divide both sides of the equation by $\displaystyle 3$.

$\displaystyle \frac{3T}{3}=\frac{351}{3}$

Solve.

$\displaystyle T=117$

The farmer can get $\displaystyle 117\ \text{turnips}$.