To find an integer ratio, let's find the fractions with a common denominator. This will be . Then, we multiply the left by  and the right by  to get fractions of  and . With the same denominators, we just have numerators to compare. Ratio is then .

If there are  girls and  boys, that means we have  students in the class. To continue to have this ratio, we need an answer than is a multiple of . 

 is a multiple of  which is the right answer.

In the problem, the drink is  espresso since the overall weight of the drink is  ounces. If we are reducing the concentration of espresso to , then we can create an equation to figure out the addition of water.

  represents the addition of water.

Cross-multiply.

Subtract  on both sides. 

If Jill, Jack and John get , that means there are  parts.

Because they found , each part gets  or .

Jack gets  or .

John gets  or .

Since the question is asking how much more did Jack get than John, we subtract  and  to get .

You don't need to solve for the actual number of broken or unbroken dolls. Instead, put the percentages in the ratio because no matter what, the percentages are fixed regardless of amount of dolls broken or unbroken.

So the question is asking for broken to unbroken. The percentage of broken dolls is .

So we have a ratio of  or . 

We need to understand that there is a total of  ounces of solution in a pot. Out of that solution,  ounces is sugar. If we add  ounces of sugar, we are also changing the volume of the pot. There is a total of  ounces of sugar and a total volume of  ounces.

To find percentage, we do  which is .

Since the problem is focusing on Carol, we will only worry about Carol's contribution to the bill.

The original split on the bill was  with Carol paying the smaller portion. With  parts, each one was . This was originally the amount Carol was responsible for.

With the the ratio of , this meant there are  parts with each being . Carol pays instead .

The difference is then  or . 

To solve this problem, first convert the fraction into a decimal, by dividing one by eight:

Then you can convert the decimal into a percentage, by putting the first two digits in the tens and ones digit of the percent (respectively), and any ensuing digits after a decimal for the percentage. Or in otherwords multiply the decimal by 100:

To solve this problem, first you have to convert the fraction into a decimal, which you can do by dividing three by seven:

The decimal appears to be non-repeating, non-terminating, but that's irrelevant, as the problem cautioned you to round to the nearest tenth of a percent.  You can convert to a percent, the first two digits of the decimal will be the percentage, and the third will be the tenth of a percent place, and the fourth will determine whether you round up or down:

%

To convert, first divide four by three:

 repeating

Now, to convert the decimal into a percentage, the ones digit becomes the hundredes digit of the percentage, and the others follow suit.  As the decimal above is repeating, and repeats at three, when you round to the nearest tenth a percent, you will have a three as your final digit:

%