A pie is made up of   crust,  apples,  sugar, and the rest is jelly. What is the ratio of crust to jelly?

To compute this ratio, you must first ascertain how much of the pie is jelly. This is:

Begin by using the common denominator :

So, the ratio of crust to jelly is:

This can be written as the fraction:

, or 

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying: 

To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:

Recall that division of fractions requires you to multiply by the reciprocal:

, 

which is the same as:

This is the same as the ratio:

Begin by manipulating the ratios into whole numbers. Let's begin with the ratio of seniors to freshmen. For every three-eights of a senior, there is one-half of a freshman:

In order to get rid of the denominators, multiply both sides by 8. Then our ratio becomes

or

.

For every three seniors, there are four freshmen. Now let's do freshman to junior:

Multiply both sides by four to get rid of the denominator. Our ratio now becomes

.

For every 8 freshmen, there are 3 juniors. To find our final ratio, let's combine our previous two ratios by finding a common term (in this case freshmen). Because the ratio of seniors to freshmen is 3:4 and the ratio of juniors to freshmen is juniors is 8:3, multiply both sides of the first ratio to make the freshmen terms match.

Our new ratios now look like this:

6 seniors: 8 freshmen

8 freshmen: 3 juniors

Combine the two ratios using the common term:

6 seniors: 8 freshmen: 3 juniors

Take out the middle term:

6 seniors: 3 juniors

Therefore the ratio of seniors to juniors is  making the ratio of juniors to seniors .

First, compute the new number of philosophy books.  This will be .  

The ratio of philosophy books to history books is thus:

This can be reduced by dividing the numerator and the denominator by :

Therefore, the ratio is .

27 of the 72 cars are 4-wheel drive, we can write this as a proportion.

The proportion of the 4-wheel drive cars to the total number of vehicles. 

Therefore, to find the proportion of 2-wheel drive cars is,

 Therefore the ratio of 2-wheel drive:4-wheel drive vehicles is 5:3.

One remote is defective for every 199 non-defective remotes.

Begin by making your life easier: presume that there are  papers on the desk. Immediately, we know that there are  paper clips. Now, if there are  papers, you know that there also must be  greeting cards. Technically you figure this out by using the ratio:

By cross-multiplying you get:

Solving for , you clearly get .

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

 papers

 paper clips

 greeting cards

Therefore, you have  total items.  Based on this, your ratio of paper clips to total items is:

, which is the same as .

To begin, you need to calculate how many students are taking Old Norse. This is:

Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:

Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of :

This is the same as .

To begin, you need to do a simple addition to find the total number of flowers in the garden:

Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by . This is:

Next, reduce the fraction by dividing out the common  from the numerator and the denominator:

This is the same as .