With a complex fraction like this, begin by simplifying the numerator of the first fraction:

Next, find the common denominator of the numerator's fractions:

Next, simplify the left division by multiplying by the reciprocal:

Finally, combine the fractions:

Simplifying, this is:

In this problem we are adding complex fractions. The first step is to add the whole numbers preceding the fractions. . Next we need to find a common denominator to add the fractions. This should be the smallest number that has all of the other denominators as a factor. The least common denominator in this case is 30. Now we need to multiply the top and bottom of each fraction by the number that will make the denominator 30. From here we can add and divide the top and bottom by two to simplify.

From here we have an improper fraction so we must subtract the value of the denominator from the numerator to make a complex fraction. After subtracting once we get a proper fraction. 

.

Since we subtracted once, that means we have a 1 attached to the fraction and can be added to the other 10 to make 11. Then to get the final answer we combine the whole numbers and the fraction to get .

Simplify both sides first.  simplifies to 6.  simplifies to . Finally 6   = .

When multiplying fractions, we can simply multiply the numerators and then multiply the denominators. Therefore,  is equal to 

We then do the same thing again, giving us .

Now we must find the least common denominator, which is .

We multiply the top by  and the bottom by . After we do this we can multiply our numerator by the reciprocal of the denominator.

Therefore our answer becomes,

  .

Begin by simplifying the denominator:

Then, you perform the division by multiplying the numerator by the reciprocal of the denominator:

Do your simplifying now:

Finally, multiply everything:

Generally, when you multiply fractions, it is a very easy affair. This does not change for complex fractions like this. You can begin by simply multiplying the numerators and denominators directly. Thus, you know:

Now, simplify this to:

 or 

Now, remember that when you divide fractions, you multiply the numerator by the reciprocal of the denominator:

Now, cancel your terms immediately:

, which is easy to finish:

The total volume is 5 * 5 * 4 = 100 cm³ . Half of this is 50 cm³ which is 50 mL.

This is a rate problem. We need to first find out how many treats a day the dog eats. Then to find the number of treats the dog eats in  days, we multiply the number of days by the number of treats a day the dog eats.

From the given information, we know that the dog eats  treats a day.

Then we multiply that number by the number of days.

Now simplify.

The total drink is made up of . Therefore, for a problem like this, you can set up a ratio:

First, simplify the right side of the equation:

Next, solve for :

.  Therefore, the total amount of drink is .

To begin with, you need to compute what is going to be your limiting factor. For the cream, you can make:

 servings.

For the coffee, you can make:

 servings. 

Therefore, this second value is your total number of servings. (You must choose the minimum, for it will be what limits your beverage-making.)

So, you know that each drink is .  If you can make  servings (remember, no partial servings!), you can make a total of .